A ball rises to surface at a constant velocity in liquid whose density is 3 times greater than that of the material of the ball. The ratio of force of friction acting on the rising ball to its weight is

Step-by-step solution

The ball is moving with constant velocity. Therefore, the net force acting on it is zero. The weight of the ball = W = 4 3 r ^3 _ b g ...(i) ....(acting downwards) As the ball is rising up, the viscous force F_v will be in the downward direction. The buoyant force F_B= 4 3 r^3 _l g ....(acting upwards) array ll & F _ v +W=F_B & ~F _ v = F _ B - W = 4 3 r ^3 g ( _l- _ b ) & F _ v = 4 3 r ^3 ~g 2 _ b ( _l=3 _ b )...(ii) array F_v W = 4 3 r^3 ~g 2 _b 4 3 r^3 _b g = 2 1 [From(i) and (ii)]