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Law of Conservation of Mechanical Energy

A simple pend...

Question

A simple pendulum of length $l$ and mass $m$ is initially at its lowest position. It is given the minimum horizontal speed necessary to move in a circular path about the point of suspension. The tension in the string at the lowest position of the bob is

A

3 m g

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B

4 m g

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C

5 m g

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D

6 m g

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Solution

The correct option is B $6 m g$
Equation of motion, $m a_{c} = T - m g$ where $a_{c} = \frac{v^{2}}{r}$
$T = \frac{m v^{2}}{r} + m g$
Also as the bob completes the vertical motion i-e, $v = \sqrt{5 g r}$
$⟹ T = \frac{m (5 g r)}{r} + m g = 6 m g$

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