Displacement of COM:Application

Q.

A block of mass 'M' is placed on the top of a bigger inclined plane of mass '10M' as shown in figure. All the surfaces are frictionless. The system is released from rest. Find the distance moved by the bigger block at the instant the smaller block reaches the ground.

1. 0.2m

2. 0.4m

3. 0.1m

4. 0.3m

Q.

The motion of centre of mass of a system of two particles is unaffected by their internal forces

1. irrespective of the actual direction of the internal forces.

2. only if they are along the line joining the particles.

3. only if they are at right angles to the line joining the particles.

4. only if they are obliquely inclined to the line joining the particles.

Q.

A cart of mass M is tied at one end of a massless rope of length 10 m. The other end of the rope is in the hands of a man of mass M. The entire system is on a smooth horizontal surface. Initially, the man is at x = 0 and the cart at x = 10 m. If the man pulls the cart using the rope, the man and the cart will meet at the point

1. x = 0

2. x = 5 m

3. x = 10 m

4. They will never meet.

Q.

If a man of mass M jumps to the ground from a height h and his centre of mass moves a distance of x during the impact, the average force acting on him (assuming his retardation to be constant during his impact with the ground) is

1. $\frac{Mgh}{x}$

2. $\frac{Mgx}{h}$

3. $Mg{\left(\frac{h}{x}\right)}^2$

4. $Mg{\left(\frac{x}{h}\right)}^2$

Q. A cart of mass 'M' is at rest on a frictionless horizontal surface and a pendulum bob of mass 'm' hangs from the roof of the cart. The string breaks, the bob falls on the floor, makes several collisions on the floor and finally lands up in a small slot made on the floor. The horizontal distance between the string and the slot is 'L'. Find the displacement of the cart during this process.

1. $\frac{Ml}{M+m}$ to the right
2. $\frac{Ml}{M+m}$ to the left
3. $\frac{ml}{M+m}$ to the right
4. $\frac{ml}{M+m}$ to the left

Q.

A child is standing at one end of a long trolley moving with a speed v on a smooth horizontal track. If the child starts running towards the other end of the trolley with a speed u, the centre of mass of the system (trolley + child) will move with a speed

1. Zero

2. (v + u)

3. (v - u)

4. v

Q.

Inside a hollow uniform sphere of mass 'M', a uniform rod of lenght 'R$\sqrt{2}$' is released from the state of rest. The mass of the rod is same as that of the sphere. If the inner radius of the hollow sphere is 'R' then find out horizontal displacement of sphere with respect to earth in the time in which the rod becomes horizontal.

1. 
   

2. 

3. 

4. 

Q.

A mon of mass 'm' moves on a plank of mass 'M' with a constant velocity 'u' with respect to the plank (as shown in the figure). If the plank rests on a smooth horizontal surface, then determine the final velocity of the plank.

1. 

2. 

3. 

4. u

Q. Two balls A and B of equal masses are projected upward simultaneously, one from the ground with speed 50 $m{s}^{-1}$ and other from height 40 m above the first ball high tower with initial speed 30 $m{s}^{-1}$. Find the maximum height attained by their centre of mass.

1. 80 m
2. 20 m
3. 100 m
4. 60 m

Q. Mr. Verma (50 kg) and Mr. Mathur (60 kg) are sitting at the two extremes of a 4 m long boat (40 kg) standing still in water. To discuss a mechanics problem, they come to the middle of the boat. Neglecting friction with water, how far does the boat move in the water during the process?

1. 2 m
2. 3/15 m
3. 2/15 m
4. 1/15 m