A block of mass $m = 2 k g$ is moving with velocity $v_{0}$ towards a massless unstretched spring of force constant $k = 20 N / m$ . Coefficient of friction between the block and the ground is $μ = 0.2$ . Find the maximum value of $v_{0}$ , so that after pressing the spring the block does not return back but stop there permanently.

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$\sqrt{\frac{26}{5}} m / s$

$\sqrt{\frac{28}{5}} m / s$

$\sqrt{\frac{5}{26}} m / s$

$3 \sqrt{\frac{1}{5}} m / s$

answer is D.

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Detailed Solution

Block will stop there if $k x = μ m g \Rightarrow x = \frac{μ m g}{k}$

$\frac{m v^{2}}{2} = \frac{k x^{2}}{2} + μ m g (x + 1) \Rightarrow v = \sqrt{\frac{26}{5}} m / s$

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