Question

A particle of mass 1 kg is projected upwards with velocity 60 m/s. Another particle of mass 2 kg is just dropped from a certain height. Find out the acceleration and the velocity of COM after 2 s when neither of the particles has collided with the ground.

• A. $-10m/s^2,20m/s$
• B. $-10m/s^2,30m/s$
• C. $-5m/s^2,20m/s$
• D. $-5m/s^2,60m/s$

Answer 1

The correct option is A $-10m/s^2,20m/s$

We know that,
a = $\frac{[m1a1+m2a2]}{[m1+m2]}$ and
u =$\frac{[m1u1+m2u2]}{[m1+m2]}$

So,

a = $\frac{[m1a1+m2a2]}{[m1+m2]}$

=$\frac{\left[\right(1)\ast (-10)+2\ast (-10\left)\right]}{3}$

=$-10m/s^2$

u =$\frac{[m1u1+m2u2]}{[m1+m2]}$

=$\frac{\left[\right(1)\ast (60)+(2)\ast (0\left)\right]}{3}$ = $20m/s$

From the above observation we conclude that, acceleration of the centre of mass will be $-10m/s^2$ and velocity of the centre of mass will be $20m/s$.