The volume of a metal sphere increases by 0.1 | vedclass

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(B) The coefficient of volume expansion $\gamma$ is related to the change in volume by the formula: $\frac{\Delta V}{V} = \gamma \Delta T$.Given that

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$2.0 	imes 10^{-5} /^{\circ}C$

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(B) The coefficient of volume expansion $\gamma$ is related to the change in volume by the formula: $\frac{\Delta V}{V} = \gamma \Delta T$.Given that the volume increases by $0.15\%$,we have $\frac{\Delta V}{V} = \frac{0.15}{100} = 0.0015$.The change in temperature is $\Delta T = 24\,^{\circ}C$.Substituting these values,we get $\gamma = \frac{\Delta V}{V \Delta T} = \frac{0.15}{100 	imes 24} = \frac{0.0015}{24} = 6.25 	imes 10^{-5} /^{\circ}C$.For a solid,the coefficient of volume expansion $\gamma$ is related to the coefficient of linear expansion $\alpha$ by the relation $\gamma = 3\alpha$.Therefore,$\alpha = \frac{\gamma}{3} = \frac{6.25 	imes 10^{-5}}{3} \approx 2.08 	imes 10^{-5} /^{\circ}C$.Rounding to the nearest provided option,we get $\alpha = 2.0 	imes 10^{-5} /^{\circ}C$.

The volume of a metal sphere increases by $0.15\%$ when its temperature is raised by $24\,^{\circ}C$. The coefficient of linear expansion of the metal is:

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