Q 11-06-125JEE MainJEE Main 2023 (8 Apr, Shift 2)Medium
A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity $3\ \text{m s}^{-1}$ (as shown in figure). Maximum height with respect to the initial position covered by it will be ______ cm. (take $g=10\ \text{m s}^{-2}$)
Numerical value type. Enter your answer.
Answer: 75
For a rolling hollow sphere $K=\tfrac12mv^2\left(1+\tfrac23\right)=\tfrac56mv^2=7.5m$ (J). It rolls up until all of this becomes potential energy:
$$mgh=7.5m\ \Rightarrow\ h=0.75\ \text{m}=75\ \text{cm}$$
Solution by Sreeraj P, M.Sc Physics