The kinetic energy of a particle executing S.H.M. is 16 , J when … - Vidyadip

MCQ

The kinetic energy of a particle executing $S.H.M.$ is $16\, J$ when it is in its mean position. If the amplitude of oscillations is $25\, cm$ and the mass of the particle is $5.12\, kg$, the time period of its oscillation is

✓
$\frac{\pi }{5}\,sec$
B
$2\pi \,sec$
C
$20\pi \,sec$
D
$5\pi \,sec$

✓

Answer

Correct option: A.

$\frac{\pi }{5}\,sec$

a
(a) At mean position, the kinetic energy is maximum.
Hence $\frac{1}{2}m{a^2}{\omega ^2} = 16$
On putting the values we get $\omega = 10\; \Rightarrow \;T = \frac{{2\pi }}{\omega } = \frac{\pi }{5}\sec $

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