MHT CET202525 Apr 2025Evening ShiftPhysicsThermal Properties of MatterActual
The volume of a metal sphere increases by 0.33 % when its temperature is raised by 50^ C . The coefficient of linear expansion of the metal is
Options
- A2.2 10⁻⁵ / ^ C
- B6.6 10⁻⁵ / ^ C
- C13.2 10⁻⁵ / ^ C
- D19.8 10⁻⁵ / ^ C
Correct answer
A. 2.2 10⁻⁵ / ^ C
Step-by-step solution
The volume expansion follows V = V₀ T , where is the coefficient of volumetric expansion. With a 0.33 % volume increase, we have V V₀ = 0.0033 . The temperature change is T = 50^ C , so 0.0033 = 50 , yielding = 6.6 10⁻⁵ / ^ C . For isotropic materials, = 3 , where is the linear expansion coefficient. Solving gives = 6.6 10⁻⁵ 3 = 2.2 10⁻⁵ / ^ C . This corresponds to option A: A .