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A small sphere falls from rest in a visc...

A small sphere falls from rest in a viscous liquid. Due to frication, heat is produced. Find the relation between the rate of production of heat and the radius of the sphere at terminal velocity.

A

`r^3`

B

`r^2`

C

`r^5`

D

`r^4`

Text Solution

Verified by Experts

The correct Answer is:
C
Rate of heat produced (power) = `(dQ)/(dt)=F_v v_T`
`implies (dQ)/(dt)=6 pi eta r v_T xx v_T`
Since, `v_T=(2r^2)/(9eta)(rho-sigma)g, (dQ)/(dt) prop r^5`
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