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A solid sphere, of radius R acquires a t...

A solid sphere, of radius R acquires a terminal velocity ` v_1 ` when falling (due to gravity) through a viscous fluid having a coefficient of viscosity ` eta ` he sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity ` v _2 ` when falling through the same fluid, the ratio ` (v_1//v_2 ) ` equals:

A

27

B

`1//27`

C

`1//9`

D

9

Text Solution

Verified by Experts

The correct Answer is:
D
`M = rho xx (4)/(3) pi R^(3)`
`(M)/( 27) = rho xx (4)/( 3) pi R^(3)`
`r to (R)/(3)`
`v_(T) prop ("Radius")^(2)`
`(v_(T))/( v_("new")) = (R^(2))/( (R // 3) ^(2)) = 9`
`v_("new") = (v_(T))/( 9)`
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