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Work Energy Theorem Application

A simple pend...

Question

A simple pendulum consists of a light string from which a spherical bob of mass, $M$ , is suspended. The distance between the point of suspension and the center of bob is $L$ . At the lowest position, the bob is given tangential velocity of $\sqrt{5 g L}$ . The K.E of the bob when the string becomes horizontal is:

A

0

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B

\frac{M g L}{2}

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C

\frac{3 M g L}{2}

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D

\frac{5 M g L}{2}

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Solution

The correct option is B $\frac{3 M g L}{2}$
From Work Energy Theorem,
$(W D)_{G} = K_{f} - K_{i}$ , where $(W D)_{G}$ is work done by gravity
$- M g L = \frac{- 1}{2} M \times 5 g L + K_{i}$

$K_{i} = \frac{3}{2} M g L$

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