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A small block of mass m is pushed towards a movable wedge of mass $m$ and height $h$ with initial velocity $u$ . All surfaces are smooth. The minimum value of $u$ for which the block will reach the top of the wedge

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$\sqrt{g h}$

$\sqrt{2 g h}$

$2 \sqrt{g h}$

None of these

answer is C.

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Detailed Solution

${\vec{P_{}}}_{s y s} = c o n s t$

$m u = 2 m v_{0} . . . (i)$

M.E conserved

$\frac{1}{2} m u^{2} = m g h + 2 (\frac{1}{2} m {v_{0}}^{2}) \frac{1}{2} m u^{2} = m g h + m (\frac{u^{2}}{4}) \frac{1}{4} m u^{2} = m g h u = 2 \sqrt{g h}$

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