A pendulum is executing simple harmonic motion and its maximum ki… - Vidyadip

MCQ

A pendulum is executing simple harmonic motion and its maximum kinetic energy is $K_1$. If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is $K_2$ then

✓
${K_2} = 2{K_1}$
B
${K_2} = \frac{{{K_1}}}{2}$
C
${K_2} = \frac{{{K_1}}}{4}$
D
${K_2} = {K_1}$

✓

Answer

Correct option: A.

${K_2} = 2{K_1}$

a
Maximum kinetic energy at lowest point $B$ is given by

$\mathrm{K}=\mathrm{mg} \ell(1-\cos \theta)$

where $\theta=$ angular amp.

$\mathrm{K}_{1}=\mathrm{mg} \ell(1-\cos \theta)$

$\mathrm{K}_{2}=\mathrm{mg}(2 \ell)(1-\cos \theta)$

$\mathrm{K}_{2}=2 \mathrm{K}_{1}$

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