Prove that if the change of temperature of a pendulum is `DeltaT` then the change in time period t will be `Deltat=1/2alphatDeltaT`. When `alpha=` coefficient of linear expansion.

Prove that the change in the time period t of a simple pendulum due to a change DeltaT of temperature is, Deltat=1/2alphatDeltaT , where alpha = coefficient of linear expansion.

Prove that, the expansion of volume V of a solid due to a rise Deltat in temperature is DeltaV=3alphaV*Deltat . Here, alpha= coefficient of linear expansion of the solid.

Show that the change in density rho of a liquid, due to rise in temperature Deltat , can be written as Deltarho=-rhogammaDeltat " ["gamma= coefficient of real expansion of the liquid].

A uniform metallic circurlar disc of mass M and radius R, mounted on frictionless bearings, is rotating at an angular speed omega about an axis passing through its centre and perpendicular to its plane. The temperature of the disc is then increased by Deltat . If alpha is the coefficient of linear expansion of the metal.

What will be the change in time period of a loaded spring, when taken to moon?

When the temperature of a body increases from t to t+Deltat , the moment of inertia of it increases from I to I+DeltaI . If the coefficient of linear expansion of the body is alpha, then show that (DeltaI)/I=2alphaDeltat .

A uniform rod of length L pivoted at one end P is freely rotated in a horizontal plane with an angular velocity omega about a vertical axis passing through P. If the temperature of the system is increased by Delta T , angular velocity becomes omega/2 . If coefficient of linear expansion of the rod is alpha (altlt1) , then DeltaT will be

A pendulum clock loses 12 s a day if the temperature is 40^(@)C and gains 4 s a day if the temperature is 20^(@)C . The temperature at which the clock will show correct time, and the coefficient of linear expansion (alpha) of the metal of the pendulum shaft are respectively

A metre scale made of steel is to be so graduated that at any temperature a reding of 1 mm should be correct up to 0.0005 mm. What can be the maximum allowed change in temperature while marking the millimetre gaps? Coefficient of linear expansion of steel =13.22 times 10^(-6@)C^(-1).