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Q.

A bullet of mass m moving with velocity v0 hits a wooden plank A of mass M placed on a smooth horizontal surface. The length of the plank is ℓ. The bullet experiences aconstant resistive force F inside the block. The minimum value of v0 such that it is able to come out of the plank is

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a

Fℓ/mM2

b

2Fℓ(M+m)Mm

c

2FℓmM2

d

Fℓ(M+m)Mm

answer is B.

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Detailed Solution

From Newton's third law a force F acts on the block in forward direction. Acceleration of block a1=FM Retardation of bullet a2=FmRelative retardation of bulletar=a1+a2=F(M+m)Mm Applying v2=u2−2arℓ0=v02−2F(M+m)Mm⋅ℓTherefore, minimum value of v0 isor  v0=2Fℓ(M+m)Mm
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