13.Oscillations
medium

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

A

$g/k\;metres$

B

$g\;metres$

C

$k/g\;metres$

D

$2\pi\;metres$

(AIPMT-1994)

Solution

Mass $(m)=5 kg$ and

time period $(T)=2 \pi$ sec.

Therefore time period $T=2 \pi \times \sqrt{\frac{m}{k}} \Rightarrow \sqrt{\frac{5}{k}}=1$

or $k=5 N / m$.

According to Hooke's Law, $F=-k l$.

Therefore decrease in length $(l)=-\frac{F}{k}=-\frac{5 g}{5}$ $=-g$ metres

Standard 11
Physics

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