Assume that, the drag force on a football depends only on the density of the air, velocity of the ball and the cross-sectional area of the ball. Balls of different sizes but the same density are dropped in an air column. The terminal velocity reached by balls of masses 250   g and 125   g are in the ratio

Step-by-step solution

Given, drag force F d depends on air density σ , velocity of ball v and area of cross-section of ball A . ∴ F d ∝ σ a v b A c Substituting dimensions of different physical quantities, we have M L T - 2 = M L - 3 a L T - 1 b   L 2 c Equating dimensions of fundamental quantities, we have a = 1 . . . . i - 3 a + b + 2 c = 1 . . . . ii - b = - 2 ⇒ b = 2 . . . . iii Putting the values of a and b in Eq (ii), we get ⇒ - 3 × 1 + 2 + 2 c = 1 ⇒ c = 1 ∵ a = 1 , b = 2 , c