A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is -

A satellite is moving with a constant speed v in circular orbit around the earth. An object of mass ‘m’ is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is -

To get output 1 at R, for the given logic gate circuit the input values must be

In the given circuit the cells have zero internal resistance. The currents (in Amperes) passing through resistance R₁ and R₂ respectively, are -