Properties of Matter 1 Question 9

9. 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 TM. If the Young’s modulus of the material of the wire is Y, then 1Y is equal to (g = gravitational acceleration )

(2015 Main)

(a) [1(TTM)2]AMg

(b) [(TMT)21]MgA

(c) [1(TMT)2]AMg

(d) [(TMT)21]AMg

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Answer:

Correct Answer: 9. (d)

Solution:

T=2πLgTM=2πL+ΔLg

Here, ΔL=FLAY=MgLAY

TM=2πL+MgLAYg

Solving Eqs. (i) and (ii), we get

1Y=AMg[(TMT)21]Δl=FLAY=FL(πr2)YΔlLr2Δl1Δl2=L/R22L/(2R)2=2



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