Question

IN A FREE SPACE , A RIFLE OF MASS M SHOOTS A BULLET OF MASS m AT A STATIONARY MASS M DISTANCE D AWAY FROM IT. WHEN THE BULLET HAS MOVED THROUGH A DISTANCE d TOWARDS THE BLOCK , THE CENTRE OF MASS OF BLOCK - BULLET SYSTEM IS AT A DISTANCE OF ?

Answer 1

Answer on Question #40895, Physics, Mechanics

IN A FREE SPACE, A RIFLE OF MASS M SHOOTS A BULLET OF MASS m AT A STATIONARY MASS M DISTANCE D AWAY FROM IT. WHEN THE BULLET HAS MOVED THROUGH A DISTANCE d TOWARDS THE BLOCK, THE CENTRE OF MASS OF BLOCK - BULLET SYSTEM IS AT A DISTANCE OF?

Solution

If $x$ is distance moved by rifle when bullet has traveled through a distance $d$, then

$$M x = m d \rightarrow x = \frac {m d}{M}.$$

So, distance of bullet from block is $D - d$ and distance between block and rifle is $D + x$.

Distance of center of mass from block in

$$r = \frac {M \cdot 0 + m (D - d)}{m + M} = \frac {m (D - d)}{m + M}.$$

Answer: $\frac{m(D - d)}{m + M}$ from the block.