AIIMS 2018 Physics Energy Conservation MCQ Question

To find the height attained by the sphere, we use the principle of conservation of energy. The initial kinetic energy (KE) of the sphere, which is a combination of translational and rotational energy, is given by $KE = \frac{7}{10} mv^2$ for a solid sphere. Substituting $m = 2 \, \text{kg}$ and $v = 10 \, \text{m/s}$, we find $KE = \frac{7}{10} \times 2 \times 10^2 = 140 \, \text{J}$. This energy is converted into gravitational potential energy (PE) at height $h$, where $PE = mgh$. Setting $140 = 2 \times 9.8 \times h$ and solving for $h$ gives $h \approx 7.1 \, \text{m}$, confirming option C.

Options A and B are incorrect because they suggest heights that are significantly higher than the calculated value, while option D ("None of these") is also incorrect as option C provides the correct answer.