A rod is of length 30m, insulated at both ends. The temperature of the rod is given by T = x (30-x) where x is length. Prove that the rate of change of temperature at the mid point of the rod vanishes.

The temperature in celsius in along rod of length 10m, insulated at both ends , is a function of length x given by T=x(10-x) . Prove that the rate of changes of temperature at the midpoint of the rod is zero .

If the radius and length of a copper rod are both doubled, the rate of flow of heat along the rod increases

Two particles of mass m each are attached to a light rod of length d, one at its centre and the other at a free end, The rod is fixed at the other end and is rotated in a plane at an angular speed omega . Calculate the angular momentum of the particle at the end with respect to the particle at the centre

The temperature gradient in a rod of 0.5 m long is 80° C/m. IF the temperature of hotter end of the rod is 30°C, then the temperature of the cooler end is

The heat is flowing through two cylindrical rods of same material. The diameters of the rods are in the ratio 1:2 and their lengths are in the ratio 2:1. If the temperature difference between their ends is the same, the ratio of rate of flow of heat through them will be

One end of a rod length 20cm is inserted in a furnace at 800K. The sides of the rod are covered with an insulating material and the other end emits radiation like a blackbody. The temperature of this end is 750K in the steady state. The temperature of the surrounding air is 300K. Assuming radiation to be the only important mode of energy transfer between the surrounding and the open end of the rod, find the thermal conductivity of the rod. Stefan constant sigma=6.0xx10^(-1)Wm^(-2)K^(-4) .

The length l meters of a metal rod at temperature theta^(@)C is given by l=2 + 0.5theta + 0.4 theta^(2) . Determine the rate of change of length with respect to temperature (i) where theta = 100^(@)C , (ii) when theta = 20^(@)C .

Two identical uniform rods AB and CD, each of length L are jointed to form a T-shaped frame as shown in figure. Locate the centre of mass of the frame. The centre of mass of a uniform rod is at the middle point of the rod.