Thermal Engineering, Refrigeration & Power

Option analysis:

• Correct physical calculation yields $40\text{ V}$.
• As per official NTA final key, Option 2 ($30\text{ V}$) is awarded.

In size reduction and milling engineering, Kick's law states that the energy required for producing analogous changes of reduction in size of geometrically similar bodies is proportional to the volume or mass of the body ($E = K_K \ln(L_1/L_2)$). Kick's law is based strictly on stress analysis of elastic deformation prior to fracture.

Option analysis:

• Kick's law: Correct, derived from the theory of elastic and plastic deformation within elastic limit.
• Rittinger's law: Based on the premise that energy consumed is proportional to the new surface area created.
• Bond's law: Based on crack-tip strain energy propagation ($E \propto 1/\sqrt{L_2} - 1/\sqrt{L_1}$).
• Planck's law: Governs blackbody spectral radiation, unrelated to milling.

In rotational kinematics, the linear tangential velocity ($V$) of a particle moving in a circular path of radius $r$ rotating with an angular velocity $\omega$ is given by the cross product relation: $\vec{V} = \vec{\omega} \times \vec{r}$, which in scalar magnitude is $V = \omega \times r$ (or $V = r\omega$).

Option analysis:

• $V = \frac{\omega}{r}$: Dimensionally incorrect.
• $V = \omega \times r$: Correct, standard kinematic vector and scalar expression.
• $V = \frac{r}{\omega}$: Inverted ratio, dimensionally incorrect.
• $V = \sqrt{\omega \times r}$: Incorrect functional form.