NEET Exam  >  NEET Notes  >  DC Pandey Solutions for NEET Physics  >  DC Pandey Solutions: Units, Dimensions & Vectors - 2

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics PDF Download

Q31. Which one is a vector quantity?
(a) Time
(b) Temperature
(c) Flux density
(d) Magnetic field intensity

Magnetic field intensity.
Option (d) is correct.Vector Quantity has both Magnitude and DirectionVector Quantity has both Magnitude and Direction


Q32. Given that P = 12,Q = 5 and R =13 also DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics then the angle between DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics will be
(a) π 
(b) π/2
(c) zero
(d) π/4

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
∴ Angle between DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
Option (b) is correct.


Q33. The forces, which meet at one point but their lines of action do not lie in one plane, are called 
(a) non-coplanar non-concurrent forces 
(b) non-coplanar concurrent forces 
(c) coplanar concurrent forces 
(d) coplanar non-concurrent forces

non-coplanar concurrent forces


Q34. Given that DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics Two out of the three vectors are equal in magnitude. The magnitude of the third vector is √2 times that of the other two. Which of the following can be the angles between these vectors? 
(a) 90°, 135°, 135° 
(b) 45°, 45°, 90° 
(c) 30°, 60°, 90° 
(d) 45°, 90°, 135°

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics …(i) 
Let Q2 = P2 and R = P√2
Thus, Eq. (i) takes the form
P2 + P2 + 2PQcos θ = 2P2 
or 2PQcos θ = 0
or cosθ = 0
or  θ = 90°
∴ Angle between DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
or P2 + R2 + 2PR cos φ = Q2
or 2PR cos φ = Q2 - P2 - R2
or   2PR cos φ = - R2
or   2P cos φ = - R
or    2P cos φ = - P√2
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
∴ φ = 135°

∴  Angle between DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
Option (a) is correct.


Q35. The angle between DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
(a) 90° 

(b) between 0° and 180°
(c) 180° only
(d) None of these

Angle (φ) between DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
Angle φ between DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
This implies that angle between DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics and DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics will vary from 0 to π.
Option (b) is correct.


Q36. Two vectors of equal magnitude have a resultant equal to either of them, then the angle between them will be 
(a) 30° 
(b) 120° 
(c) 60° 
(d) 45°

R2 = P2 + Q2 + 2PQcosθ
for R = P = Q
P2 = P2 + P2 + 2PPcos θ
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
or    θ = 120°
Option (b) is correct.


Q37. A forceDC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics newton acts on a body and displaces it by DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physicsmetre. The work done by the force is 
(a) 5 J 
(b) 25 J 
(c) 10 J 
(d) 30 J

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
= 25 J
Option (b) is correct.


Q38. If the vectors DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics are perpendicular to each other then the positive value of a is 
(a) zero 
(b) 1 
(c) 2 
(d) 3

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
Other value is - ive.
Option (d) is correct.


Q39. The angles which the vector DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics makes with the co-ordinate axes are
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
(d) none of the above

If a vector makes angles α, β and γ with the co-ordinate axes, then
cos2 α + cos2 β + cos2 γ = 1
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
∴ Option (a) is correct.


Q40. Unit vector parallel to the resultant of vectors DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
(d) None of these

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics and DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
Option (b) is correct.


Q41. The value of n so that vectors DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics may be coplanar, will be 
(a) 18 
(b) 28 
(c) 9 
(d) 36

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
∴ Vectors DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics will be coplanar if their scalar triple product is zero i.e.,

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
or 65 - 4n + 7 = 0
or  n = 18
Option (a) is correct.


Q42. Which one of the following statement is false? 
(a) A vector has only magnitude, whereas a scalar has both magnitude and direction 
(b) Distance is a scalar quantity but displacement is a vector quantity 
(c) Momentum, force, torque are vector quantities 
(d) Mass, speed and energy are scalar quantities

A vector has only magnitude, whereas a scalar has both magnitude and direction


Q43.DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics are two vectors then the value of DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
Option (a) is correct.


Q44. The angle between the two vectors DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
(a) 60° 
(b) 0° 
(c) 90° 
(d) None of these

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
= 0
⇒ θ = 90°
Option (c) is correct.


Q45. Maximum and minimum values of the resultant of two forces acting at a point are 7 N and 3 N respectively. The smaller force will be equal to 
(a) 5 N 
(b) 4 N 
(c) 2 N 
(d) 1 N

A + B = 7
A - B = 3
∴ B = 2 N
Option (c) is correct.


Q46. The component of vector DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics along the vectorDC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
(a) 5/√2
(b) 10/√2
(c) 5 √2
(d) 5

Angle between DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
and  DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
Component of  DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
Option (a) is correct.


Q47. The resultant of two forces 3P and 2P is R. If the first force is doubled then the resultant is also doubled. The angle between the two forces is 
(a) 60° 
(b) 120° 
(c) 70° 
(d) 180°

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
Option (b) is correct.


Q48. The resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is 
(a) 120° 
(b) 60° 
(c) 90° 
(d) 150°

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
As   θ = 90°, tan α = ∞
∴ P + Q cos α  = 0
i.e., DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
∴ α = 120°
Option (a) is correct.


Q49. Three vectors satisfy the relation DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics is parallel to
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics …(i)
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics …(ii)
From Eq. (i) and Eq. (ii), we conclude that DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics is perpendicular to the plane containing 

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
This implies that DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics is perpendicular to DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
Option (c) is correct.


Q50. The sum of two forces at a point is 16 N. If their resultant is normal to the smaller force and has a magnitude of 8 N. Then two forces are 
(a) 6N, 10N 
(b) 8 N, 8 N 
(c) 4 N, 12N 
(d) 2 N, 14N

P2 + Q2 + 2PQ cos α = R2 
or P2 + Q2 + 2PQ cos α = 82
or P2 + Q2 + 2PQ + 2PQ cos α - 2PQ = 64
or (P + Q)2 + 2 PQ (cos α - 1) = 64
or   (16)2 + 2 PQ (cos α - 1) = 64
or   2 PQ (cos α - 1) = - 192
or   PQ cos α - PQ = - 96 …(i)

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
(as θ = 90°)
∴ P + Q cos α = 0
Qcos α = -P …(ii)
Using Eq. (ii) and Eq. (i),
P (- P) - PQ = - 96

or - P (P + Q) = - 96
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
P = + 6 N
∴ Q = 10 N
Option (a) is correct.


Q51.DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics then the value of DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
(a) (A2 + B2 + AB)1/2
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
(c) (A + B)
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
⇒ tan θ = √3
⇒ θ = 60°
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
= A2 + B2 + 2AB cos 60°
= A2 + B2 + AB
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics


Q52. If the angle between the vectorsDC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics the value of the product DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physicsis equal to
(a) BA2 cos θ
(b) BA2 sin θ
(c) BA2 sin θ cos θ
(d) zero

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics is perpendicular to both DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
Option (d) is correct.


Q53. If a vector DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics is perpendicular to the vector DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics then the value of α is
(a) -1 
(b) 1/2
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
(d) 1

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
⇒ - 8 + 12 + 8a = 0
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
Option (c) is correct.


Q54. Minimum number of vectors of unequal magnitudes which can give zero resultant are 
(a) two 
(b) three 
(c) four 
(d) more than four

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics


Q55. The (x, y, z) coordinates of two points A and B are given respectively as (0, 3, - 1) and (- 2, 6, 4). The displacement vector from A to B is given by
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
Option (c) is correct.


Q56. The sum of two vectors DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics is at right angles to their difference. Then 
(a) A = B 
(b) A = 2B
(c) B = 2A
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics have the same direction

Using answer to questions no. 35, as angle between DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
A2 + B2 cos 2θ = 0
or  A2 = - B2 cos 2θ
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
or  A2 = - B2 cos π
or   A2 = B2
⇒ A = B
Option (a) is correct.


Match the Columns

Q1. Column-I shows some vector equations. Match column I with the value of the angle between A and B given in column II.

Column IColumn II
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics(p) zero
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics(q) π/2
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics(r) π/4
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics(s) 3π/4

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
Thus, (a) → (r) (s).

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics (given)
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
or sin θ = - sin θ
or   2 sin θ = 0
⇒ θ = 0 rad
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
or  DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
or DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics

Section-II
Subjective Questions 

Q1. Young’s modulus of steel is 2.0 x 1011 N / m2. Express it in dyne/cm2.

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics


Q2. Surface tension of water in the CGS system is 72 dynes/cm . What is its value in SI units

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics


Q3. In the expression y = a sin (ωt + θ), y is the displacement and t is the time. Write the dim ensions of a, ω and θ.

[a] = [y] = [L]
Sol: [wt] = [M0L0 T0] ∴ [ω] = [T-1]

[θ] = [M0L0 T0]


Q4. The relation between the energy E and the frequency v of a photon is expressed by the equation E = hv, where h is Planck’s constant. Write down the SI units of h and its dimensions.

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics


Q5. Write the dimensions of a and b in the relation.
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
where P is power, x is distance and t is time.

[b] = [x2] = [L2]
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics


Q6. Check the correctness of the relation DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics where u is initial velocity, a is acceleration and St is the displacement of by the body in tth second.

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
Here t in second. Hence the given equation seems to be dimensionally incorrect. But it is correct because 1 is hidden.


Q7. Let x and a stand for distance. DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics dim ensionally correct?

LHS is dimensionless. While RHS has the dimensions [L-1].


Q8. In the equation 
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
Find the value of n.

LHS is dimensionless. Hence n = 0.


Q9. Show dimensionally that the expression, DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics is  dimensionally correct, where  Y is Young’s modulus of the material of wire, L is length of wire, Mg is the weight applied on the wire and l is the increase in the length of the wire.

Just write the dimension of different physical quantities.


Q10. The energy E of an oscillating body in simple harmonic motion depends on its mass m, frequency n and amplitude a. Using the method of dimensional analysis find the relation between E, m, n and a.

E = kmxnyaz.

Here k = a dimensionless constant
∴ [E] = [m]x [n]y [a]z
∴ [ML2 T–2] = [M]x[T–1]y[L]z
∴ x = 1, y = 2 and z = 2


Q11. The centripetal force F acting on a particle moving uniformly in a circle may depend upon mass (m), velocity (v) and radius r of the circle. Derive the formula for F using the method of dimensions.

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
(k = a dimensionless constant) 
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
Solving we get,
x = 1, y = 2 and z = - 1
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics


Q12. Taking force F, length L and time T to be the fundamental quantities, find the dimensions of (a) density, (b) pressure, (c) momentum and (d) energy.

[d] = [F]x [L]y [T]z
∴ [ML–3] = [MLT–2]x[L]y[T]z 
Equating the powers we get,
x = 1, y = - 4, z = 2
∴ [ d] = [FL–4 T2]
Similarly other parts can be solved.

Vectors

Q13. Find the cosine of the angle between the vectors DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics


Q14. Obtain the angle between DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
Angle between DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics


Q15. Under what conditions will the vectors DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics be perpendicular to each other ?

Their dot product should be zero.


Q16. Deduce the condition for the vectors DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics

Ratio of coefficients of DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics should be same.


Q17. Three vectors which are coplanar with respect to a certain rectangular co-ordinate system are given by
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
Find
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
(c) Find the angle between DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics

No solution is required.


Q18. Find the components of a vector DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics along the directions of 

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics


Q19. If vectors DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics be respectively equal to DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics Find the unit vector parallel to DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics


Q20. If two vectors are DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics By calculation, prove that 

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics is perpendicular to both DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics


Q21. Find the area of the parallelogram whose sides are represented by 

Area of parallelogram DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics


Q22. The resultant of two vectors DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics is at right angles toDC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics and its magnitude is half of DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET PhysicsFind the angle between DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics


Q23. The x and y-components of vector DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics are 4 m and 6 m respectively. The x and y-components of vector DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics are 10 m and 9 m respectively. Calculate for the vector DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics the following
(a) its x andy-components 
(b) its length 
(c) the angle it makes with x-axis

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics


Q24. Prove by the method of vectors that in a triangle 
DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
Applying sine law, we have

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics


Q25. Four forces of magnitude P, 2P, 3P and AP act along the four sides of a square ABCDm cyclic order. Use the vector method to find the resultant force.

DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics


Q26. DC Pandey Solutions: Units, Dimensions & Vectors - 2 | DC Pandey Solutions for NEET Physics
R2 + S2 = 2(P2 + Q2)

R2 = P2 + Q2 + 2PQ cos θ
S2 = P2 + Q2 - 2PQ cos θ
∴ R2 + S2 = 2 (P2 + Q2)

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FAQs on DC Pandey Solutions: Units, Dimensions & Vectors - 2 - DC Pandey Solutions for NEET Physics

1. What are the units and dimensions of physical quantities?
Ans. Units are the standards of measurement used to express the magnitude of physical quantities, while dimensions represent the nature of the physical quantity and are expressed in terms of fundamental quantities such as length, mass, and time.
2. How do you convert between units of physical quantities?
Ans. To convert between units of physical quantities, we can use conversion factors or conversion formulas. For example, to convert from meters to kilometers, we divide the value in meters by 1000.
3. What is the significance of vectors in physics?
Ans. Vectors are used in physics to represent quantities that have both magnitude and direction, such as velocity, force, and displacement. They help in understanding and analyzing the physical phenomena involving direction and can be added or subtracted using vector algebra.
4. How do you add and subtract vectors?
Ans. To add or subtract vectors, we use the parallelogram law or the triangle law. In the parallelogram law, we draw the vectors as adjacent sides of a parallelogram and the resultant vector is the diagonal of the parallelogram. In the triangle law, we draw the vectors as sides of a triangle and the resultant vector is the closing side of the triangle.
5. What are the different types of vector products?
Ans. The different types of vector products are dot product, also known as scalar product, and cross product, also known as vector product. The dot product gives a scalar quantity and is the product of the magnitudes of the vectors and the cosine of the angle between them. The cross product gives a vector quantity and is the product of the magnitudes of the vectors, the sine of the angle between them, and a unit vector perpendicular to the plane containing the vectors.
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