When the temperature of a body increases form t to t+Δt, its moment of inertia increases from I to I+ΔI. The coefficient of linear expansion of the body is α . The ratio ΔI/I is :
A
Δt/t
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B
2Δt/t
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C
αΔt
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D
2αΔt
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Solution
The correct option is D2αΔt Moment of inertia is given by mr2 where r= perpendicular distance of the centre of mass of the body from the rotational axis. If I1 andI2 are initial and final moment of inertia for a change in temperature dt, we can write, I2−I1I1=r22−r12r12=((1+αdt)2−1)=2αdt+α2dt2 Neglecting value of α2, we get I2−I1I1=2αdt