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)`
B. ` 6 xx 10 ^(-5)`
C. ` 18 xx 10 (-5)`
D. ` 1.2 xx 10 ^(-5)`

Answer

A

Explanation

` Delta V = V gamma Delta t `
` rArr " " 0.24 = 100 xx gamma xx 40 `
` gamma = (0.24)/(100 xx 40 )`
` " " = 0.00006`
` " " = 6 xx 10 ^(-5)`
` alpha = (gamma)/(3)`
`rArr " " alpha = 2 xx 10^(-5) //""^(@)C `