A clock with a metallic pendulum gains `5 s` each day at a temperature of `15^@C` and loses `10 s` each day at a temperature of `30^@C`. Find the coefficient of thermal expansion of the pendulum metal.

Options

A. `2.3 xx 10^(-5)//.^(@)C`
B. `4.2 xx 10^(-5)//.^(@)C`
C. `5.6 xx 10^(-5)//.^(@)C`
D. `8.4 xx 10^(-5)//.^(@)C`

Answer

B

Explanation

Tension 'T' at a distance x from axis.
`T=(m)/(l)(l-x)[omega^(2)(x+(l-x)/(2))]`
Stress = y strain
`(T)/(A)=Y(dDeltal)/(dx)=intdDeltal=int(T)/(AY)dx`
`Deltal=(1)/(AY)int(m)/(2l)(l^(2)-x^(2))omega^(2)dx`
`Deltal=(m)/(2AYl)omega^(2)underset(0)overset(l)int(l^(2)-x^(2))dx`
`Deltal=(momega^(2))/(2AYl)(l^(3)-(l^(3))/(3))`
`Deltal=(momega^(2))/(2AYl)(2l^(3))/(3)=(momega^(2)l^(2))/(3AY)`