A thin rod having length `L_0` at `0^@C` and coefficient of lineare expansion `alpha` has its two ends maintained at temperatures `theta_1` and `theta_2`, respectivley. Find its new length.

Find out the increase in moment of inertia I of a uniform rod coefficient of linear expansion alpha about its perpendicular bisector when its temperature is slightly increased by DeltaT .

The radius of a metal sphere at room temperature T is R, and the coefficient of linear expansion of the meta is alpha . The sphere is heated a little by a temperature DeltaT so that its new temperature is T + DeltaT . The icnrease in the volume of the sphere is approximately

Two conductors have the same resistane at o^@C but their temperature coefficiencts of resistance are alpha_1 and alpha_2 . Find the repective temperature coefficients of their series and parallel combinations.

A point particle of mass M is attached to one end of a massless rigid non-conducting rod of length L. Another point particle of the same mass is attached to the other end of the rod. The two particles carry charges +q and -q respectively. This arrangement is held in a region of a uniform electric field E such that the rod makes a small angle theta (say of about 5 degree) with the field direction, fig. Find an expression for the minimum time needed for the rod to become parrallel to the field after it is set free.

A uniform rod a has mass M and length L.Its radius of gyration about an axis through its one end and perpendicuular to its length is :

Find a real number theta, 0 < theta < pi/2 , which increases twice as fast as its sine.

At 0^(@)C the resistance of conductor of a conductor B is n times that of condoctor A temperature coefficient of resistance for A and B are alpha_(1) and alpha_(2) respectively the temperature coefficient of resistance of a circiut segment constant A and B in series

Rachel, an engineering student, was asked to make a model shaped like a cyclinder. with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model the Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.)

A thin straight rod of length I, has uniform linear charge density lambda . Moving at a constant speed v, the rod enters a cube of sides having length L through its left fae and leaves through the right face as shown in the figure Find the maximum electric flux through the cube.