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A pendulum made of a uniform wire of cro...

A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to `T_(M)` If the Young's modulus of the material of the wire is Y then `1/Y` is equal to
(g = gravitational acceleration)

A

`[((T_(M))/T)^(2)-1](Mg)/A`

B

`[1-((T_(M)/T)^(2)]A/(Mg)`

C

`[1-(T/(T_(M))^(2)]A/(M_(g))`

D

`[((T_(M))/T)^(2)-1]A/(Mg)`

Text Solution

Verified by Experts

The correct Answer is:
D
`T=2pisqrt(l/g)` …(1)
`T_(M)=2pisqrt((l+Deltal)/g)` ..(2)
`Y=(Fl)/(ADeltal)rArrDeltal=(Mgl)/(AY)` ..(3)
`rArr1/Y=A/(Mg)[((T_(M))/T)^(2)-1]`
So correct choice is (d.).
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