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): When two solid spheres of the same material but different radii are dropped from rest into a long column of a given viscous liquid, they will have the same initial acceleration. Reason (R): The terminal velocity of a sphere falling through a viscous medium is independent of its radius. In the light
Options
- ABoth (A) and (R) are correct and (R) is the correct explanation of (A)
- BBoth (A) and (R) are correct but (R) is not the correct explanation of (A)
- C(A) is correct but (R) is not correct
- D(A) is not correct but (R) is correct
Correct answer
C. (A) is correct but (R) is not correct
Step-by-step solution
Assertion (A) is correct. The initial acceleration of a sphere dropped in a viscous liquid is determined by the net force at t=0 , where velocity and viscous drag are zero. The acceleration is a = mg - F_b m = g (1 - ) , where is the density of the material and is the density of the liquid. This expression is independent of the radius of the sphere. Reason (R) is incorrect. According to Stokes' law, the terminal velocity is given by v_t = 2r^2( - )g 9 . Thus, terminal velocity is directly proportional to the square