NEET
- Exam
- NEET
- Subject
- Physics
- Chapter
- Rotational Motion
NEET · Physics · Rotational Motion
If radius of the earth is reduced to half without changing its...
If radius of the earth is reduced to half without changing its mass, then match the following columns
(
)
| Column I | Column II | ||
| (A) | Angular momentum | (p) | Will become two times |
| of the earth | |||
| (B) | Time period of rotation | (a) | Will become four times |
| of the earth | |||
| (C) | Rotational kinetic energy | (r) | Will remain constant |
| of the earth | |||
| (s) | None of the above |
Options
- Aa-r b-s c-p
- Ba-s b-r c-p
- Ca-r b-s c-q
- Da-q b-p c-s
Correct answer
C. a-r b-s c-q
Step-by-step solution
In the absence of external torque, angular momentum remains constant.
(\begin{gathered}
L=I \omega=\text{ constant } \\
I \propto R^2
\end{gathered})
(\therefore I) will remain (\frac{1}{4}) th or (\omega) will become 4 times.
Therefore, time period () will remain (\frac{1}{4}) th
Further,
(K=\frac{L^2}{2 I})
Since, angular momentum is constant and I has become (\frac{1}{-} \mathrm{th}).
Therefore, kinetic energy will become 4 times.