Question

Two solid spheres of same metal but of mass M and 8M fall simultaneously on a viscous liquid and their terminal velocitied are v and n v, then value of n is
A. 16
B. 8
C. 4
D. 2

Answer 1

Correct Answer - C
Mass = volume x density
`:. M=(4)/(3)pi r^(3)xxrho`
or `M prop r^(3)` or `r prop M^(1//3)`
`:. (r_(1))/(r_(2)) =((M_(1))/(M_(2)))^(1//3) =(1)/(2)`
Terminal velocity, `v=(2r^(2)(rho-sigma)g)/(9eta) i.e., v prop r^(2)`
`:. (v_(1))/(v_(2)) =((r_(1))/(r_(2)))^(2)` or `(v)/(nv) =((1)/(2))^(2) =(1)/(4)`
or `n=4`