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`

Options

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

A

Explanation

As `V_(T) = V_(0) (1 + gamma Delta T):. (V_(T) - V_(0))/(V_(0)) = gamma Delta T`
or `(0.24)/(100) = 40 gamma or 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)`