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): Two spheres of the same material and radii R and 2R fall through the same viscous liquid. When they attain their respective terminal velocities, the ratio of the viscous drag forces on them is 1 : 8 . Reason (R): The viscous drag force on a sphere moving at its terminal velocity is directly proport
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
A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
Step-by-step solution
According to Stokes' law, the viscous drag force is given by F_v = 6 r v . The terminal velocity v_t of a sphere of radius r and density falling in a liquid of density and viscosity is given by v_t = 2 9 r^2( - )g . Therefore, the terminal velocity is directly proportional to the square of the radius ( v_t r^2 ). Substituting this into Stokes' law, we get F_v r(r^2) F_v r^3 . Thus, the Reason is correct. For two spheres of radii R and 2R , the ratio of their viscous drag forces at terminal velocity will be R^3 : (2