A pendulumd made of a uniform wire of cross sectional area (A) has time T.When an additionl 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:

Options

A. (a) `[1-(T_(M)/T)^(2)]A/M_(g)`
B. (b) `[1-(T/T_(M))^(2)]A/M_(g)`
C. (c ) `[(T_(M)/T)^(2)-1]A/M_(g)`
D. (d) `[(T_(M)/T)^(2)-1]M_(g)/A`

Answer

C

Explanation

(c ) As we know, time period, `T=2pisqrtl/g`
When additional mass (M) is added then
`T_(M) =2pisqrt(l+Deltal)/g`
`T_(M)/T =sqrt(l+Deltal)/l or (T_(M)/T)^(2) =(l+Deltal)/l`
or, (T_(M)/T)^(2) =1(Mg)/(Ay)` [:. Deltal=(Mgl)/(Ay)]`
:. 1/y=[(T_(M)/T)^(2)-1]A/(Mg).