Multiple Choice Question. Two hailstones with radii in the ratio of 1:4 fall from a great height through the atmosphere. Then the ratio of their terminal velocities is

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Two hailstones with radii in the ratio of 1:4 fall from a great height through the atmosphere. Then the ratio of their terminal velocities is 1:16 Explanation: Let r1 and r2 be the radius of two hailstones falling from a great height through atmosphere then: From question, r_1/r_2 = $\frac{1}{4}$ .....(i) We have an expression for the velocity of moving body in the atmosphere as: v = $\frac{2}{9}$ r^2g (d_2 - d_1)/n Where, r, g, d1 and d2 are radius of the body, acceleration due to gravity, the density of the body, density of medium respectively. Therefore, v oo r^2 If v1 and v2 are the velocity of hailstones 1 and 2. The expression for the ratio of their velocity will be: v_1/v_2 = r_1^2/r_2^2 Thus, from the equation (i) v_1/v_2 = r_1^2/r_2^2 v_1/v_2 = (r_1/r_2)^2 v_1/v_2 = ($\frac{1}{4}$)^2 v_1/v_2 = $\frac{1}{16}$

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