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A steel ball of 50mm radius is kept on a...

A steel ball of `50mm` radius is kept on a hole of concrete. The diameter of the hole is `0.05mm` less then the diameter of the steel ball at `20^(@)C`. Coefficient of volume expansion of the steel ball is `3.2x 10^(-6)//^(@)C` . At what temperature the ball will be inside the hole ?

A

`30^(@)C`

B

`55^(@)C`

C

`65^(@)C`

D

`70^(@)C`

Text Solution

Verified by Experts

The correct Answer is:
D
A steel ball ………..
`D_(s)-D_(H) = 0.05mm`
Where `D_(s)` is diameter of ball and `D_(H)` is diameter of ball hole. As we increase temperature
`D_(H)gtD_(s)` for ball to enter hole
`D_(H)(1+12xx10^(-6)DeltaDeltaT)-D_(s)(1+(3.2)/(3)xx10^(-6)Delta T)gt0`
`(12xx10^(-4)- (3.2)/(3)xx10^(-4))Delta Tgt0.05`
Given `Delta T gt 46^(@)`
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