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A homogeneous rod of length $l = n x$ and mass $M$ is lying on a smooth horizontal floor. A bullet of mass $m$ hits the rod at a distance $x$ from the middle of the rod at a velocity $v$ perpendicular to the rod. If the velocity of the farther end of the rod just after impact is in the opposite direction of $v$ then which of the following can be a value of $n$ ?

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$5$

$3$

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$7$

answer is A, B, C.

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Detailed Solution

If farther point is at rest,

$\frac{l^{2}}{12} = k^{2} = \frac{l}{2} \times \frac{l}{n}$

$n = 6$
if $n < 6$ , direction is opposite to $v$ .

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