A body of mass 4kg hangs from a spring and oscillates with a period 0.5s on the removal of the body, the springs is shortened by

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6.3 cm

0.63 cm

6.21 cm

0.62 cm

answer is C.

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Detailed Solution

Time period $T = 2 π \sqrt{\frac{m}{k}}$

$∵ mg = kx ∴ T = 2 π \sqrt{\frac{x}{g}} \Rightarrow {(0.5)}^{2} = 4 π^{2} \times \frac{x}{9.8} \Rightarrow \frac{{(0.5)}^{2} \times 9.8}{4 \times 3.14 \times 3.14} = x \Rightarrow x = 0.0621 m \Rightarrow x = 6.21 cm$

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