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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
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B
6×105K1
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C
18×105K1
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D
1.2×105K1
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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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