Displacement of COM:Application

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

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 art. The string breaks, the bob falls on the floor, makes several collisions on the floor and finally lands up in a small slot made in the floor. The horizontal distance between the string and the slot is L. Find the displacement of the cart during the process ?

1. $\frac{3mL}{m+M}$

2. $\frac{mL}{M+m}$

3. $\frac{4mL}{M+m}$

4. $\frac{2mL}{M+m}$

Q. Find the displacement of the wedge when the mass 'm' has comes out of the wedge. There is no friction anywhere.

1. $\frac{ml}{M+2m}$
2. $\frac{ml}{M+m}$
3. $\frac{ml-mlcos\theta }{M+2m}$
4. $\frac{ml+mlcos\theta }{M+2m}$

Q.

Two masses - ' $\sqrt{3}$m' and '$\sqrt{2}$m' are tied by a light string are placed on a wedge of mass '4m'. The wedge is placed on a smooth horizontal surface. Find out the value of $\theta$ such that the wedge does not move even after the system is set free from the state of rest.

1. ${30}^{\circ }$

2. ${45}^{\circ }$

3. ${60}^{\circ }$

4. none of these

Q. A block was released on the convex surface of hemispherical wedge as shown in the figure below. Determine the displacement of the wedge when the block reaches the angular position $\theta$.

1. $\frac{mRcos\theta }{M+m}$ to the right
2. $\frac{mRsin\theta }{M+m}$ to the right
3. $\frac{mRcos\theta }{M+m}$ to the left
4. $\frac{mRsin\theta }{M+m}$ to the left

Q. Figure below shows the system is at rest initially with x = 0. A man and a woman both are initially at the extreme ends of the platform. The man and the woman start to move towards each other. Obtain an expression for the displacement 's' of the platform when the two meet in terms of the displacement '$x_1$' of the man relative to the platform.

1. $\frac{m_1{x}_1+m_{2}l}{m_1+m_2+m_0}$
2. $\frac{m_1{x}_1-m_{2}l}{m_1+m_2+m_0}$
3. $\frac{m_1{x}_1+m_2(l-x_1)}{m_1+m_2+m_0}$
4. $\frac{m_1{x}_1-m_2(l-x_1)}{m_1+m_2+m_0}$

Q.

Consider a two-particle system with the particles having masses $m_1$ and $m_2$. If the first particle is pushed towards the centre of mass by a distance 'd', by what distance should the second particle be moved so as to keep the centre of mass at the same position?

1. ($\frac{m_1{m}_2}{m_1+m_2}$)d

2. $\frac{m_2}{m_1}$d

3. $\frac{m_1}{m_2}$d

4. ($\frac{m_1-m_2}{m_1+m_2}$)d

Q. Mohit is on a camping trip with his father. He wants to catch a fish using a javelin. He can see the fish at an angle of 30° (as shown). At what angle should he throw his javelin so that he can catch the fish?

1. More than ${30}^{\circ }$
2. Less than $30{}^{\circ }$
3. At ${30}^{\circ }$

Q.

Cosider a gravity - free hall in which a tray of mass M , carrying a cubical block of ice of mass m and edge L , is at rest in the middle. If the ice melts, by what distance does the centre of mass of "the tray plus the ice" system descent ?

1. $\frac{-mL}{2(M+m)}$

2. $\frac{-mL}{2(M+m)}$

3. Zero

4. $\frac{-2mL}{3(M+m)}$

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. $\frac{R}{2}$

2. $\frac{R}{4}$

3. $\frac{R}{2}$ $\sqrt{2}$
   

4. $\frac{R}{\sqrt{2}}$

Q. A lever of length 14 cm has its load arm 5 cm long and effort arm is 9 cm long. (a) To which class does it belong? (b) Draw diagram of the lever showing the position of fulcrum F and directions of both the load L and effort E. (c) What is the mechanical advantage and velocity ration if the efficiency is 100% ? (d) What will be the mechanical advantage and velocity ration if the efficiency becomes 50%?

Q. What are the factors upon which the centre of gravity of a body depends