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A small steel ball of radius r is allowe...

A small steel ball of radius r is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity `eta`. After some time the velocity of the ball attains a constant value known as terminal velocity `upsilon_T`. The terminal velocity depends on (i) the mass of the ball m (ii) `eta`, (iii) r and (iv) acceleration due to gravity g . Which of the following relations is dimensionally correct?

A

`V prop (mgr)/(eta)`

B

`V prop mg eta r`

C

`V prop (mg)/(eta r)`

D

`V prop (eta mg)/(r )`

Text Solution

Verified by Experts

The correct Answer is:
C
`F=6pi eta ` rv i.e., v has the dimensions of `(F)/(eta r) " or" (mg)/(eta r)`
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