UPSEE Solved Model Paper 4

Consider two identical homogeneous balls, A and B, with the same initial temperatures. One of them is at rest on a fixed horizontal surface, while the second one hangs on a thread as shown. Now the same amount of heat has been supplied to both the balls. We assume that such quantities as specific heat and coefficient of thermal expansion are constant (i.e., do not depend on temperature) and positive. Also, we neglect the expansion in the length of the string and take all kinds of heat losses from balls to be negligible. Considering the loss in gravitational potential energy is converted into heat energy and vice versa, the final temperature of the balls, TA and TB will obey the relation?