A bullet of mass a and velocity b is fired into a large block of wood of mass c. The final velocity of the system is

\frac{c b}{a + b}

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\frac{b}{c} (a + b)

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\frac{a b}{a + c}

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\frac{b}{a} (a + c)

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Solution

The correct option is B $\frac{a b}{a + c}$
Given : Mass of bullet $m_{b} = a$
Mass of wood $m_{w} = c$
Initial velocity of bullet $u = b$
Let the final velocity of the "wood + bullet" system be $V$
Applying conservation of momentum:
$m_{b} u + 0 = (m_{b} + m_{w}) V$
$a b = (a + c) V$ $⟹ V = \frac{a b}{a + c}$

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A bullet of mass a and velocity b is fired into a large block of wood of mass c. The final velocity of the system is

The correct option is B aba+cGiven : Mass of bullet mb=a Mass of wood mw=c Initial velocity of bullet u=bLet the final velocity of the "wood + bullet" system be VApplying conservation of momentum: mbu+0=(mb+mw)Vab=(a+c)V ⟹V=aba+c