Question

A body of mass 5 kg hangs from a spring and oscillates with a time period of $2\pi$ second. If the body is removed, the length of the spring will decrease by

• A. $glk$ metre
• B. $klg$ metre
• C. $2\pi$ metre
• D. $g$ metre

Answer 1

The correct option is D $g$ metre

For a spring mass system, the time period is given by$,$

$T=2\pi \surd \left(m/k\right)$

where$,m=$ mass $=5kg$

$k=$ spring constant

Putting the values given$,$

$2\pi =2\pi \surd 5/k$

$=k=5N/m$

After the body is removed, let the length of the spring be reduced by $x$ meter$.$

so$,$ the restoring force should be equal to the weight of the body$.$

$kx=mg$

$=5x=5\times 9.8$

$=x=9.8m$ $(g=9.8)$

Hence,

option $\left(D\right)$ is correct answer.