Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): When two solid spheres of the same material but radii r and 2r fall in a viscous liquid, the viscous drag force on the larger sphere at terminal velocity is 8 times that on the smaller sphere. Reason (R): The viscous drag force on a sphere at terminal velocity is directly proportional to the cube o

Step-by-step solution

At terminal velocity, the net force on the falling sphere is zero. The viscous drag force ( F_v ) exactly balances the effective weight of the sphere (actual weight minus buoyant force). F_v = W - F_B F_v = 4 3 r^3 g - 4 3 r^3 g F_v = 4 3 r^3 ( - ) g For a given material (constant ) and liquid (constant ), the viscous drag force at terminal velocity is directly proportional to the volume of the sphere, and hence to the cube of its radius ( F_v r^3 ). Therefore, Reason (R) is correct. Using this proportionality for