Moment of inertia of a cylinder of mass M, length L and radius R about an axis passing through its centre and perpendicular to the axis of the cylinder is
I = $$M\left( {{{{R^2}} \over 4} + {{{L^2}} \over {12}}} \right)$$. If such a cylinder is to be made for a given mass of a material, the ratio $${L \over R}$$ for it to have minimum possible I is

In the circuit shown in the figure, the total charge is 750 $$\mu $$C and the voltage across capacitor C₂ is 20 V. Then the charge on capacitor C₂ is :

A balloon filled with helium (32^oC and 1.7 atm.) bursts. Immediately afterwards the expansion of helium can be considered as

A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth’s radius R_e . By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that it become $$\sqrt {{3 \over 2}} $$ times larger. Due to this the farthest distance from the centre of the earth that the satellite reaches is R. Value of R is :