KVPY SX SB Exam 2018 Question Paper

Question : 39 of 120

Marks: +1, -0

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 :

2 $^{1\/6 }$
2 $^{1\/3 }$
2 $^{1\/2 }$
2 $^{2\/3}$

Validate

Solution:

F ∝ ρ ^a v^ b A^c

MLT^{–2} = M^a L^{–3a} \ L^b T^{–b}L^{2c}

on solving a = 1, b = –2, c = 1

\table \so \mg = \ρv^ 2 A,\since \m = \vρ;mg = ρv^ 2 m ^{2\/3 },R ∝ m ^{1\/3};,A ∝ m^{2\/3};v ∝ m^{1\/6}

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