A mass m suspended from a vertical spring oscillates with a period of 4 s. The mass is then kept at rest. Through what dis"tan"ce the spring will be stretched ? [Take `pi^(2)=10]

Options

A. 3 m
B. 4 m
C. 5 m
D. 6 m

Answer

B

Explanation

For an oscillating mass,
`T=2pi sqrt((m)/(K))`
`therefore 4 =2pi sqrt((m)/(K)) therefore 16=4pi^(2) ((m)/(K))`
`therefore (m)/(K)=(16)/(4pi^(2))=(4)/(pi^(2))`
and when the mass is at rest, the spring is stretched through a dis"tan"ce x.
Then stretching force mg = Restoring force (Kx)
`therefore mg =Kx`
`therefore x=((m)/(K))g therefore x=(4)/(pi^(2))g =(4xx10)/(10)=4 cm`