Centre of Mass

Q.

A force of 25N acts on a body at rest for 0.2s and a force of 70N act for next 0.1s in opposite direction. If the final velocity of the body is 5m/s the mass of the body is?

Q.

Two blocks A and B of mass m and 2m are connected by a massless spring of force constant k. They are placed on a smooth horizontal plane. Spring is stretched by an amount x and then released. The relative velocity of the blocks when the spring comes to its natural length is

(a) [√(3k/2m)]x (b) [√(2k/3m)]x

(c) √(2kx/m) (d) √(3km/x)

Q.

Where is the centre of mass of the Earth-moon system?

Q. A huge rod whose length is comparable to the radius of the Earth is suspended from the sky. The centre of gravity will be at its centre of mass.

1. True
2. False

Q. A force acting on body of 1 tonne at rest. The body acquired a velocity of 1ms`1 in a distance of 10m.find the force

Q. What is the acceleration of the COM of the body?

1. 10 m/s/s
2. 5 m/s/s
3. 0 m/s/s
4. 15 m/s/s

Q.

A child sits stationary at one end of a long trolley moving uniformly with a speed V on a smooth horizontal floor. If the child gets up and runs about on the trolley in any manner, what is the speed of the CM of the (trolley + child) system?

Q. Two particles A and B of masses ${}^{\prime }{m}^{\prime }$ and ${}^{\prime }2m^{\prime }$ are suspended from two massless springs of force constants $K_1$ and $K_2$. During their oscillation, if their maximum velocities are equal, then ratio of amplitudes of A and B is :

1. $\sqrt{\frac{K_2}{2K_1}}$
2. $\sqrt{\frac{2K_1}{K_2}}$
3. $\sqrt{\frac{K_1}{K_2}}$
4. $\sqrt{\frac{K_2}{K_1}}$

Q. A mass $m$ is vertically suspended from a spring of negligible mass: the system oscillates with a frequency $n$. What will be the frequency of the system if a mass $4m$ is suspended from the same spring

1. $n/2$
2. $4n$
3. $2n$
4. $n/4$