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Standard XII

Physics

Work Energy Theorem

A bullet of m...

Question

A bullet of mass $m$ is fired with a velocity $v$ into a fixed log of wood and penetrates a distance s before coming to rest. Assuming that the path of the bullet in the log of wood is horizontal, the average resistance offered by the log of wood is

\frac{m v}{2 s^{2}}

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\frac{m v^{2}}{2 s}

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\frac{2 s}{m v^{2}}

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\frac{m s^{2}}{2 v}

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Solution

The correct option is B $\frac{m v^{2}}{2 s}$
W.D resistance $= Δ K . E$

$\to F . \to S = \frac{1}{2} m v_{f i n a l}^{2} - \frac{1}{2} m u_{i n i t i a l}^{2}$

$\to F . \to S = - \frac{1}{2} m v^{2}$

$\Rightarrow - F . s = - \frac{1}{2} m v^{2}$

$\Rightarrow F = \frac{m v^{2}}{2 s}$

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A bullet of mass m is fired with a velocity v into a fixed log of wood and penetrates a distance s before coming to rest. Assuming that the path of the bullet in the log of wood is horizontal, the average resistance offered by the log of wood is

The correct option is B mv22sW.D resistance =ΔK.E→F.→S=12mv2final−12mu2initial→F.→S=−12mv2⇒−F.s=−12mv2⇒F=mv22s

A bullet of mass $m$ is fired with a velocity $v$ into a fixed log of wood and penetrates a distance s before coming to rest. Assuming that the path of the bullet in the log of wood is horizontal, the average resistance offered by the log of wood is

The correct option is B $\frac{m v^{2}}{2 s}$
W.D resistance $= Δ K . E$

$\to F . \to S = \frac{1}{2} m v_{f i n a l}^{2} - \frac{1}{2} m u_{i n i t i a l}^{2}$

$\to F . \to S = - \frac{1}{2} m v^{2}$

$\Rightarrow - F . s = - \frac{1}{2} m v^{2}$

$\Rightarrow F = \frac{m v^{2}}{2 s}$