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Question

A simple pendulum of bob mass m is oscillating with an angular amplitude αm (in radian). The maximum tension in the string is

A
mg
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B
mgαm
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C
mgα2m
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D
mg(1+α2m)
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Solution

The correct option is D mg(1+α2m)
The tension is maximum when the bob is in the mean position and is given by T=mg+mv2l where l is the length of the string.
Now, vmax=|Aω|=(lαm)ω=lαmgl
v2max=l2α2m×gl=lgα2m
Tmax=mg+ml×lgα2m=mg(1+α2m)
Hence, the correct choice is (d).

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