A bullet of mass m is fired into a large block of wood of mass M with velocity v. The final velocity of the system is?

(\frac{m}{M - m}) v

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(\frac{m + M}{M}) v

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(\frac{M - m}{M}) v

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(\frac{m}{m + M}) v

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Solution

The correct option is D $(\frac{m}{m + M}) v$
u is initial velocity
v is finall velocity
m1 is m
m2 is M
u1 is v
u2 is 0
$v_{1} = v_{2} = v_{3}$
$t o t a l i n i t i a l m o m e n t u m = f i n a l l m o m e n t u m$
$m_{1} u_{1} + m_{2} u_{2} = m_{1} v_{1} + m_{2} v_{2}$
$m v + M \times 0 = m v_{3} + {M v}_{3}$
$m v = (m + M) v_{3}$
$v_{3} = \frac{m v}{m + M}$

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A bullet of mass m is fired into a large block of wood of mass M with velocity v. The final velocity of the system is?

The correct option is D (mm+M)vu is initial velocity v is finall velocity m1 is m m2 is M u1 is v u2 is 0 v1=v2=v3totalinitialmomentum=finallmomentumm1u1+m2u2=m1v1+m2v2mv+M×0=mv3+Mv3mv=(m+M)v3v3=mvm+M