Consider two charged metallic spheres S₁ and S₂ of radii R₁ and R₂, respectively. The electric fields E₁ (on S₁) and E₂ (on S₂) on their surfaces are such that E₁/E₂ = R₁/R₂. Then the ratio V₁ (on S₁) / V₂ (on S₂) of the electrostatic potentials on each sphere is :

A uniform sphere of mass 500 g rolls without slipping on a plane horizontal surface with its centre moving at a speed of 5.00 cm/s. Its kinetic energy is :

In the given circuit, value of Y is :

A particle of mass m is dropped from a height h above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of $$\sqrt {2gh} $$. If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of $$\sqrt {{h \over g}} $$ is :