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Block is taken toward left so that spring is compressed. Now the block is released from rest. Block moves on a smooth horizontal surface after leaving spring, then on circular path R. By how much distance spring should be compressed so that block can complete circular motion:

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$R \sqrt{10}$

$5 R$

$\frac{5}{2} R$

$R \sqrt{3}$

answer is B.

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Detailed Solution

To complete the circle the block must have a velocity of $\sqrt{5 g R}$ at the bottom of the circular path

Mechanical Energy conservation

$\frac{1}{2} {kx}^{2} = \frac{1}{2} m {(\sqrt{5 gR})}^{2}$

$\frac{mg}{2 R} x^{2} = 5 mgR$

$x = \sqrt{10} R$

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