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)

Question

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), 1 - T T M 2 A M g, T M T 2 - 1 A ⁡ Mg ⁡, T M T 2 - 1 Mg A ⁡, 1 - T M T 2 A M g

MARKS App · Accepted Answer

Initial length = l . Time period T = 2 π l g . . . ( i ) . After suspending mass M , . Youngs modulus Y = Stress Strain = F A ∆ l l = F l ∆ l A Change in length of wire Δ l = F l AY Now time period T M = 2 π l + Δ l g . . . ( ii ) T T M = 2 π l g 2 π l + Δ l g ∵ i ii T 2 T M 2 = l l + Δ l ⇒ T m 2 T 2 = 1 + ∆ l l 1 + F A Y = T m T 2 p u t t i n g v a l u e o f ∆ l 1 Y = T m T 2 - 1 A F F = M g 1 Y = T m T 2 - 1 A M g

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