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The radius of metal sphere at room tempe...

The radius of metal sphere at room temperature T is R and the coefficient of linear expansion of the metal is `alpha`. The sphere is heated a little by a temperature T, so that new temperature is `T+DeltaT`. The increase in volume of sphere is approximately

A

`2piRalphaDeltaT`

B

`piR^(2)alphaDeltaT`

C

`4piR^(3)alphaDeltaT/3`

D

`4piR^(2)alphaDeltaT`

Text Solution

Verified by Experts

d) Since, coefficient of volume expansion `gamma=3 xx ` coefficient of linear expansion
`rArr` `gamma` = `3alpha`
Now, `1/(DeltaT)((DeltaV)/(V)` = `3alpha` `rArr DeltaV` = `3V.alpha. DeltaT`
`rArr` `DeltaV= 4/3piR^(3)xx 3alpha xx DeltaT=4piR^(3)alphaDeltaT`
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