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Law of Conservation of Mechanical Energy

The length of...

Question

The length of simple pendulum is 1m and mass of its bob is $50$ gram. The bob is given sufficient velocity so that the bob describes vertical circle whose radius equal to length of pendulum. The maximum difference in the kinetic energy of bob during one revolution is:

A

0.98 J

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B

1.96 J

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C

4.9 J

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D

9.8 J

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Solution

The correct option is A $0.98 J$
$L = 1 m, m = 0.05 k g$
$V_{b} = \sqrt{5 g R} m / s$
$V_{t} = \sqrt{g R}$
the velocity is maximum at bottom
the velocity is minimum at top
$∴ Δ K E = \frac{1}{2} m [(\sqrt{5 g R})^{2} - (\sqrt{g R})^{2}]$
$= \frac{m}{2} [4 g R]$
$= 2 \times (0.05) (9.8) (1)$
$= 0.98 J$

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