NEET  >  DC Pandey Solutions: Units, Dimensions & Vectors - 3

# DC Pandey Solutions: Units, Dimensions & Vectors - 3 - Physics Class 11 - NEET

Section-II
Subjective Questions

Ques 1: Young’s modulus of steel is 2.0 x 1011 N / m2. Express it in dyne/cm2.
Ans:

Ques 2: Surface tension of water in the CGS system is 72 dynes/cm . What is its value in SI units?
Ans:

Ques 3: 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.
Ans: [a] = [y] = [L]
Sol: [wt] = [M0L0 T0] ∴ [ω] = [T-1]

[θ] = [M0L0 T0]

Ques 4: 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.
Ans:

Ques 5: Write the dimensions of a and b in the relation.

where P is power, x is distance and t is time.
Ans: [b] = [x2] = [L2]

Ques 6: Check the correctness of the relation  where u is initial velocity, a is acceleration and St is the displacement of by the body in tth second.
Ans:

Here t in second. Hence the given equation seems to be dimensionally incorrect. But it is correct because 1 is hidden.

Ques 7: Let x and a stand for distance.  dim ensionally correct?
Ans: LHS is dimensionless. While RHS has the dimensions [L-1].

Ques 8: In the equation

Find the value of n.
Ans: LHS is dimensionless. Hence n = 0.

Ques 9: Show dimensionally that the expression,  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.
Ans: Just write the dimension of different physical quantities.

Ques 10: 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.
Ans: 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

Ques 11: 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.

Ans:
(k = a dimensionless constant)

Solving we get,
x = 1, y = 2 and z = - 1

Ques 12: 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.
Ans: [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

Ques 13: Find the cosine of the angle between the vectors
Ans:

Ques 14: Obtain the angle between
Ans:

Angle between

Ques 15: Under what conditions will the vectors  be perpendicular to each other ?
Ans: Their dot product should be zero.

Ques 16: Deduce the condition for the vectors
Ans: Ratio of coefficients of  should be same.

Ques 17: Three vectors which are coplanar with respect to a certain rectangular co-ordinate system are given by

Find

(c) Find the angle between
Ans: No solution is required.

Ques 18: Find the components of a vector  along the directions of

Ans:

Ques 19: If vectors  be respectively equal to  Find the unit vector parallel to

Ans:

Ques 20: If two vectors are  By calculation, prove that

is perpendicular to both
Ans:

Ques 21: Find the area of the parallelogram whose sides are represented by
Ans: Area of parallelogram

Ques 22: The resultant of two vectors  is at right angles to and its magnitude is half of Find the angle between
Ans:

Ques 23: The x and y-components of vector  are 4 m and 6 m respectively. The x and y-components of vector  are 10 m and 9 m respectively. Calculate for the vector  the following
(a) its x andy-components
(b) its length
(c) the angle it makes with x-axis
Ans:

Ques 24: Prove by the method of vectors that in a triangle

Ans:

Applying sine law, we have

Ques 25: 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.
Ans:

Ques 26:
R2 + S2 = 2(P2 + Q2)
Ans: R2 = P2 + Q2 + 2PQ cos θ
S2 = P2 + Q2 - 2PQ cos θ
∴ R2 + S2 = 2 (P2 + Q2)

The document DC Pandey Solutions: Units, Dimensions & Vectors - 3 | Physics Class 11 - NEET is a part of the NEET Course Physics Class 11.
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## FAQs on DC Pandey Solutions: Units, Dimensions & Vectors - 3 - Physics Class 11 - NEET

 1. What are the basic units of measurement used in physics?
Ans. The basic units of measurement used in physics are the meter (m) for distance, the kilogram (kg) for mass, the second (s) for time, the ampere (A) for electric current, the kelvin (K) for temperature, the mole (mol) for amount of substance, and the candela (cd) for luminous intensity.
 2. How do you calculate dimensions of a physical quantity?
Ans. The dimensions of a physical quantity can be calculated by analyzing its units. Each unit can be expressed as a combination of fundamental units (such as length, mass, time, etc.). By equating the units on both sides of an equation, we can determine the dimensions of the physical quantity.
 3. What is a vector quantity?
Ans. A vector quantity is a physical quantity that has both magnitude and direction. Examples of vector quantities include displacement, velocity, force, and acceleration. Vectors are represented graphically with arrows, where the length represents the magnitude and the direction of the arrow represents the direction of the vector.
 4. What are the operations that can be performed on vectors?
Ans. There are three main operations that can be performed on vectors: addition, subtraction, and scalar multiplication. Vector addition involves combining the magnitudes and directions of two vectors to obtain a resultant vector. Vector subtraction is similar, but involves subtracting the magnitudes and directions. Scalar multiplication involves multiplying a vector by a scalar quantity (a number) to change its magnitude.
 5. How can vectors be resolved into components?
Ans. Vectors can be resolved into components by using trigonometry. If a vector makes an angle θ with a reference axis, the horizontal component can be found by multiplying the magnitude of the vector by cos(θ), and the vertical component can be found by multiplying the magnitude by sin(θ). These components can then be combined to reconstruct the original vector.

## Physics Class 11

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## Physics Class 11

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