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Two solids spheres of same metal having ...

Two solids spheres of same metal having masses M and 8M respectively fall simultaneously on a same viscous liquid and their terminal velocities are v and nv, then the value of 'n' is

A

16

B

8

C

4

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
Ration of the masses of the two spheres`=1:8`
So, ratio of the their volumes `=1:8`
and ratio of their radii `=1:8^(1//3)=1:2`
Thus, terminal velocity, `v=2/9(r^2(rho-sigma)g)/(eta) i.e., v prop r^2`
Hence, ratio of the terminal velocities of the two spheres
`=1:2^2=1:4=v:4v`
`therefore n=4`
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