Question

The volume of a metal sphere increases by `0.24%` when its temperature is raised by `40^(@)C` . The coefficient of linear expansion of the metal is .......... `.^(@)C`
A. `2 xx 10^(5).^(@)C^(-1)`
B. `6 xx 10^(-5).^(@)C^(-1)`
C. `18 xx 10^(-5).^(@)C^(-1)`
D. `1.2 xx 10^(-5).^(@)C^(-1)`

Answer 1

Correct Answer - A
From, `V_(T) = V_(0)(1+gammaDeltaT)`
`rArr (V_(T) -V_(0))/(V_(0)) = gammaDeltaT`
`(0.24)/(100) = gamma40 .^(@)C`
`gamma = (0.24)/(100 xx 40) = 6 xx 10^(-5) .^(@)C^(-1)`
Coefficient of linear expansion,
`alpha = (gamma)/(3) = (6 xx 10^(-5))/(3) = 2 xx 10^(-5) .^(@)C^(-1)`