Q 11-05-115JEE MainJEE Main 2023 (10 Apr, Shift 1)Medium
A closed circular tube of average radius $15$ cm, whose inner walls are rough, is kept in vertical plane. A block of mass $1$ kg just fits inside the tube. The speed of block is $22\ \text{m s}^{-1}$, when it is introduced at the top of tube. After completing five oscillations, the block stops at the bottom region of tube. The magnitude of work done by the tube on the block is ______ J. (Given $g=10\ \text{m s}^{-2}$)
Numerical value type. Enter your answer.
Answer: 245
Only gravity and the tube act. From the top (speed $22\ \text{m s}^{-1}$) to rest at the bottom ($0.3$ m lower):
$$W_{tube}=\Delta K-W_{gravity}=(0-\tfrac12\times1\times22^2)-(1\times10\times0.3)=-242-3=-245\ \text{J}$$
Magnitude $245$ J.
Solution by Sreeraj P, M.Sc Physics