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DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET

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Introductory Exercise 5.1
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Introductory Exercise 5.1

Q.1. The diagram shows a rough plank resting on a cylinder with one end of the plank on rough ground. Neglect friction between plank and cylinder. Draw diagrams to show:
(a) the forces acting on the plank,
(b) the forces acting on the cylinder.
DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET

Sol. 

N = Normal force on cylinder by plank
DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET
R = Normal force on cylinder by ground,
f = Force of friction by ground by cylinder,
w = Weight of cylinder.
N cosθ = f
w + N sinθ = R,
N(R) = Reaction to N,
DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET
(Force acting on plank)
i.e., normal force on plank by cylinder
R' = Normal force on plank by ground,
w = Weight of plank,
f' = frictional force on plank by ground.
Resultant of f' and R', N(R) and w pass through point O.


Q.2. Two spheres A and B are placed between two vertical walls as shown in figure. Friction is absent everywhere. Draw the free body diagrams of both the spheres.
DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET

Sol.
DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET
R = Normal force on sphere A by left wall,
N = Normal force on sphere A by ground,
N' = Normal force on sphere A by sphere B,
wA = Weight of sphere A.
N' cos θ = R
N' sin θ + wA = N
DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET
R' = Normal force on sphere B by right wall,
N ( R) = Reaction to N i.e. normal force on sphere B by sphere A,
wB = Weight of sphere B,
R', N(R) and wB pass through point O, the centre sphere B.


Q.3. A point A on a sphere of weight W rests in contact with a smooth vertical wall and is supported by a string joining a point B on the sphere to a point C on the wall. Draw free body diagram of the sphere.
DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET

Sol: 
N = Normal force on sphere by wall,
DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET
w = Weight of sphere,
T = Tension in string.


Q.4. Write down the components of four forces DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET along ox and oy directions as shown in Fig. 5.33.
DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET
Sol.

  1. F1x = 2√3 N
  2. F2x = -2 N
  3. F3x = 0
  4. F4x = 4 N
  5. F1y = 2N
  6. F2y = 2√3 N
  7. F3y = -6 N
  8. F4y = 0

Component of DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET
along x-axis : 4 cos 30° = 2√3 N
along y-axis : 4 sin 30° = 2 N
Component of DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET
along x-axis : 4 cos 120° = - 2 N
along y-axis : 4 sin 120° = 2√3 N
Component of DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET
along x-axis : 6 cos 270° = 0 N
along y-axis : 6 sin 270° = - 6 N
Component of DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET
along x-axis : 4 cos 0° = 4 N
along y-axis : 4 sin 0° = 0 N


Q.5. A uniform rod AB of weight w is hinged to a fixed point at A It is held in the horizontal position by a string, one end of which is attached to B as shown in Fig. 5.34. Find in terms of w, the tension in the string.

Sol: Taking moment about point A
DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET
AB = 1
(T sin 30) 1 = w 1/2
⇒ T = w


Q.6. In Question 3 of the same exercise, the radius of the sphere is a. The length of the string is also a. Find the tension in the string.

Sol. DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET

See figure (answer to question no. 3)
DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET
T cos 30° = w
or DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET
or  DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET


Q.7. Find the values of the unknown forces if the given set of forces shown in figure below are in equilibrium.
DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET
DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET

Sol. F = 10.16 newton, R = 2.4 newton

R cos 30° + 3 = f cos 60°
DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET
i.e., DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET
or  
R√3 + 6 = f …(i)
and R sin 30° + f sin 60° = 10
i.e., DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET
or R + f√3 = 20 …(ii)
Substituting the value of f from Eq. (i) in Eq. (ii)
R + ( R√3 + 6)√3 = 20
4 R + 6√3 = 20
DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET
∴   f = (2.4) √3 + 6
f = 10.16 N


Q.8. Two beads of equal masses m are attached by a string of length √2a and are free to move in a smooth circular ring lying in a vertical plane as shown in Fig. 5.36. Here, a is the radius of the ring. Find the tension and acceleration of B just after the beads are released to move.

Sol. DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET
At point B (instantaneous vertical acceleration only)
DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET
∴  mg - T sin 45° = ma …(i)
At point A (instantaneous horizontal acceleration only)
∴  T cos 45° = ma …(ii)
Combining Eqs. (i) and (ii)
mg - ma = ma
DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET 

T cos 45° = m(g/2)

T/√2 = m(g/2)

T = mg/√2

The document DC Pandey Solutions: Laws of Motion - 1 - Notes | Study Physics Class 11 - NEET is a part of the NEET Course Physics Class 11.
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