Q.

In a free space, a rifle of mass M shoots a bullet of mass m at a stationary block of mass M at a 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

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a

(D-d)mM+m from the bullet

b

md+MDM+m from the block

c

2md+MDM+m from the block

d

(D-d)MM+m from the bullet

answer is D.

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Detailed Solution

Distance between bullet and block at this instant is (D-d).Distance of CM from bullet                   =M(D-d)+m×0M+m=MM+m(D-d)Similarly, distance of CM from block = mM+m (D-d)Hence, option (4) is correct.
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