Q 11-06-220JEE MainJEE Main 2019 (9 Apr, Shift 1)Easy
The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal plane: (i) a ring of radius $R$, (ii) a solid cylinder of radius $\frac R2$ and (iii) a solid sphere of radius $\frac R4$. If, in each case, the speed of the center of mass at the bottom of the incline is same, the ratio of the maximum heights they climb is
Answer: (B) $20:15:14$
Rolling kinetic energy $\frac12mv^2\left(1 + \frac{k^2}{r^2}\right)$ becomes $mgh$, so $h \propto 1 + \frac{k^2}{r^2}$ (the radii do not matter):
- ring: $1 + 1 = 2$
- solid cylinder: $1 + \frac12 = \frac32$
- solid sphere: $1 + \frac25 = \frac75$
$$h_1:h_2:h_3 = 2:\frac32:\frac75 = 20:15:14$$
Solution by Sreeraj P, M.Sc Physics