First slide

Simple hormonic motion

Question

If the period of oscillation changes from 2 sec to 1.5 sec, and the length of simple pendulum is 1m, then the change in length is

Easy

A

Increased by $\large \frac{7}{{16}}m$
B

decreased by $\large \frac{7}{{16}}m$
C

increased by $\large \frac{9}{{16}}m$
D

decreased by $\large \frac{9}{{16}}m$

Solution

$\large \frac{{{T_1}}}{{{T_2}}}\, = \,\sqrt {\frac{{{l_1}}}{{{l_2}}}} \, = \,\frac{2}{{1.5}}\, = \,\sqrt {\frac{{{l_1}}}{{{l_2}}}} ;\,{l_2}\, = \,\frac{9}{{16}}m\,\,\,{l_1}\, = \,1m\,$
$\large \Delta {l_1}\, = \,{l_2} - {l_1}\, = \,\frac{9}{{16}} - 1\, = \, - \frac{7}{{16}}m$
So, decreases by $\large \frac{7}{{16}}m$ $\large {l_2} < {l_1}$

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