BITSAT PYQs for Centre of Mass with Solutions: Practice BITSAT Previous Year Questions

1.

A man of mass \(100 \,kg\). is standing on a platform of mass \(200 \,kg\). Which is kept on a smooth ice surface. If the man starts moving on the platform with a speed \(30 \,m/sec\) relative to the platform then calculate with what velocity relative to the ice the platform will recoil?

• 5 m/sec
• 10 m/sec
• 15 m/sec
• 20 m/sec

2.

A system consists of three particles each of mass m and located at (1,1), (2,2) and (3,3). The coordinates of the centre of mass are

• (1,1)
  
• (2,2)
  
• (3,3)
  
• (6,6)

3.

At any instant the velocity of a particle of mass 500g is \( \left( 2t \hat{i} + 3t^2 \hat{j} \right) \, \text{ms}^{-1} \). If the force acting on the particle at \( t = 1 \) s is \( \left( \hat{i} + x \hat{j} \right) \, \text{N} \), then the value of \( x \) will be:

• 3
  
• 4
  
• 6
  
• 2
  

4.

A spherically symmetric gravitational system of particles has a mass density $ \rho = \begin{cases} \rho_0 & \text{for} \; r \le R \\ 0 & \text{for} \; r > R \end{cases}$ where $r_0$ is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed $V$ as a function of distance $r (0 < r < \infty) $ from the centre of the system is represented by

5.

A system consists of three particles, each of mass \(m\) and located at \((1,1),(2,2)\) and \((3,3)\). The co-ordinates of the center of mass are :

• (1, 1)
• (2,2)
• (3,3)
• (6,6)

6.

Two particles $A$ and $B$ initially at rest, move towards each other, under mutual force of attraction. At an instance when the speed of $A$ is $v$ and speed of $B$ is $2v$, the speed of center of mass $(CM)$ is

• Zero
• V
• 2.5v
• 4v