JEE Main 2015 · 4 Apr · Shift 1 · Physics Q8

← JEE Main 2015 · 4 Apr · Shift 1

PhysicsSingle correct+4 / -1Question 8 of 90

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 $\dfrac1Y$ is equal to :

(g = gravitational acceleration)

\left[\left(\dfrac{T_M}T\right)^2-1\right]\dfrac A{Mg}

\left[\left(\dfrac{T_M}T\right)^2-1\right]\dfrac{Mg}A

\left[1-\left(\dfrac{T_M}T\right)^2\right]\dfrac A{Mg}

\left[1-\left(\dfrac T{T_M}\right)^2\right]\dfrac A{Mg}

Answer and worked solution

Official answer: A

The extra load stretches the wire by $\Delta L=\dfrac{MgL}{AY}$ . With $T\propto\sqrt L$ :
$\left(\frac{T_M}T\right)^2=1+\frac{Mg}{AY}\implies\frac1Y=\left[\left(\frac{T_M}T\right)^2-1\right]\frac A{Mg}.$

Topics:Hooke's law and elastic moduli Simple and compound pendulum

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JEE Main 2015 · 4 Apr · Shift 1, Physics question 8