NEETPhysicsMechanical Properties of Fluids
Match List-I with List-II regarding a solid sphere of radius r moving through a fluid. List-I List-II (A) Viscous force on a sphere moving at a constant given velocity (I) Proportional to r^3 (B) Terminal velocity of a solid sphere falling under gravity (II) Zero (C) Viscous force on a solid sphere falling at its terminal velocity (III) Proportional to r (D) Viscous drag on a sphere moving in an ideal fluid (IV) Prop
Options
- A(A)-(III), (B)-(I), (C)-(IV), (D)-(II)
- B(A)-(III), (B)-(IV), (C)-(I), (D)-(II)
- C(A)-(IV), (B)-(III), (C)-(I), (D)-(II)
- D(A)-(I), (B)-(IV), (C)-(III), (D)-(II)
Correct answer
B. (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
Step-by-step solution
According to Stokes' law, the viscous force on a spherical body is F = 6 r v . For a constant given velocity v , the viscous force F r . Thus, (A) matches with (III). The terminal velocity of a sphere falling under gravity is given by v_t = 2r^2( - )g 9 . Therefore, terminal velocity v_t r^2 . Thus, (B) matches with (IV). The viscous force at terminal velocity is F = 6 r v_t . Substituting v_t r^2 , we get F r(r^2) = r^3 . Thus, (C) matches with (I). An ideal fluid is non-viscous ( = 0 ). Therefore, the viscous dra