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Question: In a free space, a rifle of mass M shoots a bullet of mass m at a stationary block of mass M distanc...

In a free space, a rifle of mass M shoots a bullet of mass m at a stationary block of mass M distance D away from it. When the bullet has moved through a distance d towards the block, the centre of mass of the bullet-block system is at a distance of –

A

m(D−d)M+m\frac{m(D - d)}{M + m}from the block

B

(m+M)dM\frac{(m + M)d}{M} from rifle

C

M(D+d)M+m\frac{M(D + d)}{M + m}from bullet

D

None of these

Answer

M(D+d)M+m\frac{M(D + d)}{M + m}from bullet

Explanation

Solution

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

Mx = md ̃ x = mdM\frac{md}{M}

So, distance of bullet from block D – d and distance between block and rifle = D + x

\ Distance of C.M from block in

r1 = Mx(0)+m(D−d)m+M\frac{Mx(0) + m(D - d)}{m + M}= (D−d)mm+M\frac{(D - d)m}{m + M}

Distance of C.M from rifle

=m(x+d)+M(D+x)m+M\frac{m(x + d) + M(D + x)}{m + M}

Also distance of C.M from bullet

= m×o+M(D−d)M+m\frac{m \times o + M(D - d)}{M + m}