A sphere rolls on a horizontal surface. Is there any point of the sphere which has a vertical velocity?

A solid sphere rolls on horizontal surface without slipping. What is the ratio of its rotational to translation kinetic energy.

A plank P is placed on a solid cylinder S , which rolls on a horizontal surface. The two are of equal mass. There is no slipping at any of the surfaces in contact. The ratio of kinetic energy of P to the kinetic energy of S is:

A smooth sphere is moving on a horizontal surface with velocity vector 3hat(i) + hat(j) immediately before it hits a vertical wall. The wall is parallel to the vector hat(j) and the coefficient of restitution between the wall and sphere is (1)/(3) . The velocity vector of the sphere after it hits the wall is :-

An insulating solid sphere of radius R has a uniformaly positive charge density rho . As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinity is zero. Statement-1: Wgen a charge 'q' is taken from the centre to the surface of the sphere, its potential energy charges by (qrho)/(3 in_(0)) Statement-2 : The electric field at a distance r (r lt R) from the centre of the the sphere is (rho r)/(3in_(0))

A 1 Kg solid sphere rolls without slipping on a rough horizontal suface as shown in figure. Select incorrect alternative

Two spheres P and Q of equal radii have densities rho_1 and rho_2 , respectively. The spheres are connected by a massless string and placed in liquids L_1 and L_2 of densities sigma_1 and sigma_2 and viscosities eta_1 and eta_2 , respectively. They float in equilibrium with the sphere P in L_1 and sphere Q in L_2 and the string being taut(see figure). If sphere P alone in L_2 has terminal velocity vecV_p and Q alone in L_1 has terminal velocity vecV_Q , then

Two small and heavy spheres, each of mass M, are placed a distance r apart on a horizontal surface. The graviational potential at the mid-point on the line joining the centre of the spheres is :-

Rate of increase in surface area of a sphere w.r.t radius is ……….