A rectangular tank contains water to a height h. A metal rod is hinged to the bottom of the tank so that it can rotate freely in the vertical plane. The length of the rod is L and it remains at rest with a part of it lying above the water surface. In this position the rod makes an angle theta with the vertical. Assume that y=costheta and find fractional change in value of y when temperature of the system increases by a small value DeltaT.Coefficient of linear expansion of material of rod and the tank arealpha_(1) and alpha_(2) respectively. Coefficient of volume expansion of water is lambda. What is necessary condition for theta to increase?

A rectangular tank contains water to a height h. A metal rod is hinged

1.	A rectangular tank contains water to a height h. A metal rod is hinged to the bottom of the tank so that it can rotate freely in the vertical plane. The length of the rod is L and it remains at rest with a part of it lying above the water surface. In this position the rod makes an angle theta with the vertical. Assume that y=costheta and find fractional change in value of y when temperature of the system increases by a small value DeltaT.Coefficient of linear expansion of material of rod and the tank arealpha_(1) and alpha_(2) respectively. Coefficient of volume expansion of water is lambda. What is necessary condition for theta to increase?
Answer» Answer :`1/2 (alpha_(1)+gamma-4alpha_(2))DELTA T; 4alpha_(2) gt alpha_(1)+gamma`