Constrained Motion - NEET Physics Questions
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Constrained Motion

Question 1:

For the arrangement of pulleys shown in figure the effort (P) required to raise the given load (W) is

1. 200 N
2. 250 N
3. 800 N
4. 1000 N
View Answer

Net Force acting on the block in upward direction is 4T which will balance weight of the object. So, 

⇒ 4T= 800 N 

⇒T = 200 N

Question 2:

What are the acceleration of the blocks  A and B, shown in figure (in m/sec²)

 

1. 0,0
2. 4 m/s², 4 m/s²
3. 6 m/s², 3 m/s²
4. 4 m/s², 2 m/s²
View Answer

Writing equations of motion for the objects as,

40 - T = 4 × 2a     ---(i)

and 2T -40 = 4a    -----(ii)

Solving (i) and (ii)

a= 2 m/s²

So, acceleration of object A is 4 m/s² and for object B is 2 m/s²

Question 3:

The masses of the bodies A and B in figure are 20 kg and 10 kg, respectively. They are initially at rest on the floor and are connected by a weightless string passing over a weightless and frictionless pulley. An upward force F is applied to the pulley. Find the acceleration a1 of body A and a2 of body B when F is 340 N :

 

1. a1 = 7 m/sec², a2 = 24 m/sec²
2. a1 = 0, a2 = 0
3. a1 = 1.5 m/sec², a2 = 7 m/sec²
4. a1 = 0 m/sec², a2 = 7 m/sec²
View Answer

As F= 340 N. Force acting on object A in upward direction is F/2 i.e 170 N. This force is insufficient to pull the object upwards. (weight of A is greater than 170 N)

So, a1= 0 m/s²

Force acting on B in upward direction is 170 N and weight is 10g or 100 N. Net force in upward direction is 70 N. so,

a2= 7 m/s²

Question 4:

The block A is moving downward with constant velocity v0. Find the velocity of the block B, when the string makes an angle θ with the horizontal.

 

1. v0
2. v0 cos θ
3. v0 / cos θ
4. v0 sin θ
View Answer

When two objects are connected by a string component of velocity along the string remains equal.

v1 cosθ = v 0

⇒v1= v0/ cosθ

 

Question 5:

In the arrangement, shown in figure, pulleys A and B are massless and frictionless and threads are ideal. Block of mass m1 will remain at rest if: 

 

nlm constrained motion

1. \[ \frac{1}{m_{3}}=\frac{2}{m_{2}}+\frac{3}{m_{1}} \]
2. \[ m_{1}= m_{2}= m_{3} \]
3. \[ \frac{4}{m_{1}}=\frac{1}{m_{2}}+\frac{1}{m_{3}}\]
4. \[ \frac{1}{m_{1}}=\frac{1}{m_{2}}+\frac{1}{m_{3}}\]
View Answer

nlm constrained motion

In the movable pulley system, tension in the string connecting m2 and m3 is:

T=2m2m3gm2+m3T = \frac{2 m_2 m_3 g}{m_2 + m_3}

Since this tension acts twice to balance

m1m_1

, we equate:

2T=m1g⇒4m2m3gm2+m3=m1g2T = m_1 g \Rightarrow \frac{4 m_2 m_3 g}{m_2 + m_3} = m_1 g

Cancelling

gg

and rearranging gives:

4m1=1m2+1m3\boxed{ \frac{4}{m_{1}} = \frac{1}{m_{2}} + \frac{1}{m_{3}} }