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Question

The mass of the bob of a simple pendulum of length L is m . If the bob is left from its horizontal position then the speed of the bob and the tension in the thread in the lowest position of the bob will be respectively.

A
2gL and 3mg
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B
gL and 3mg
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C
2gL and 4mg
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D
gL and 2mg
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Solution

The correct option is A 2gL and 3mg
The given condition can be shown as

Let the speed of the bob at lowest position be v
By the conservation of energy
Potential energy at point A= Kinetic energy at point B
mgL=12mv2
v=2gL
Also, for tension in the string we have force equation as
T=mg+mv2L=mg+mL(2gL)2=3mg

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