NEETPhysicsMechanical Properties of Fluids
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): For a solid sphere of a given material falling through a viscous liquid, the viscous force acting on it at terminal velocity is directly proportional to the cube of its radius. Reason (R): The terminal velocity of a solid sphere falling through a viscous liquid is directly proportional to the cube
Options
- ABoth (A) and (R) are true and (R) is the correct explanation of (A)
- BBoth (A) and (R) are true but (R) is not the correct explanation of (A)
- C(A) is true but (R) is false
- D(A) is false but (R) is true
Correct answer
C. (A) is true but (R) is false
Step-by-step solution
At terminal velocity, the net force on the sphere is zero. The downward weight is balanced by the upward buoyant force and viscous 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 Thus, the viscous force at terminal velocity is directly proportional to r^3 . Therefore, Assertion (A) is true. According to Stokes' law, the terminal velocity v_t of a sphere is given by: v_t = 2r^2( - )g 9 This shows that terminal velocity is directly proportional to the square of the radius ( r^2 ), not the cube.