MCQ
Two point masses of mass $4m$ and $m$ respectively separated by $d$ distance are revolving under mutual force of attraction. Ratio of their kinetic energies will be :
- ✓$1 : 4$
- B$1 : 5$
- C$1 : 1$
- D$1 : 2$
✓
Answer
Correct option: A.
$1 : 4$
a
They will revolue about this centre of mass
They will revolue about this centre of mass
$0=4 m(-x)+m(d-x)$
$x=\frac{d}{5}$
They will same $\omega$
$\frac{K_{4 m}}{K_{m}}=\frac{\frac{1}{2} I_{4 m} \omega^{2}}{\frac{1}{2} I_{m} \omega^{2}} \Rightarrow \frac{K_{4 m}}{K_{m}}=\frac{I_{4 m}}{I_{m}}$
$\frac{K_{4 m}}{K_{m}}=\frac{\frac{1}{2}(4 m)(d / 5)^{2}}{\frac{1}{2}(m)(4 d / 5)^{2}} \Rightarrow \frac{K_{4 m}}{K_{m}}=\frac{1}{4}$
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