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Q.

A block is simply released from the top of an inclined plane as shown in the figure. The maximum compression in the spring when the block hits the spring is nearly _______

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a

$\sqrt{5} m$

b

2

c

$\sqrt{6} m$

d

$1 m$

answer is D.

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Detailed Solution

$m g .5 = μ m g (2 + x) + \frac{1}{2} k x^{2}$
$250 = 25 (2 + x) + \frac{1}{2} \times 50 \times x^{2}$
$250 = 50 + 25 x + 25 x^{2} \Rightarrow x^{2} + x + 2 = 10$
$x^{2} + x - 8 = 0$
$x = \frac{- 1 \pm \sqrt{1 - 4.1 (- 8)}}{2} = \frac{- 1 \pm \sqrt{33}}{2} = 2.35 ≃ 2$

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