Question

# The volume of a metal sphere increases by $$24\%$$  when its temperature is raised by $$40 K$$. The coefficient of linear expansion of the metal is:

A
2×105K1
B
6×105K1
C
18×105K1
D
1.2×105K1

Solution

## The correct option is D $$2\times { 10 }^{ -5 }{K }^{ -1 }$$FROM, $${ V }_{ T }={ V }_{ 0 }\left( 1+\gamma \Delta T \right)$$$$\Longrightarrow \quad \dfrac { { V }_{ T }-{ V }_{ 0 } }{ { V }_{ 0 } } ={ \gamma \Delta T }$$$$\dfrac { 0.24 }{ 100 } ={ \gamma 40 }$$$$\gamma =\dfrac { 0.24 }{ 100\times 40 } =6\times { 10 }^{ -5 }{ K}^{ -1 }$$Coefficient of linear expansion,$$\alpha =\dfrac { \gamma }{ 3 } =\dfrac { 6\times { 10 }^{ -5 } }{ 3 } =2\times { 10 }^{ -5 }{K }^{ -1 }$$Physics

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