JEE Mains · Physics · STD 11 - Motion in plane
- JEE Mains 2024
- Hard
- MCQ
A stone of mass \(900 \mathrm{~g}\) is tied to a string and moved in a vertical circle of radius \(1 \mathrm{~m}\) making \(10\ \mathrm{rpm}\). The tension in the string, when the stone is at the lowest point is _______. (if \(\pi^2=9.8\) and \(g=9.8 \mathrm{~m} / \mathrm{s}^2\) )
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(9.8 \mathrm{~N}\)
Step-by-step Solution
Detailed explanation
Given thaat
\( \mathrm{m}=900 \mathrm{gm}=\frac{900}{1000} \mathrm{~kg}=\frac{9}{10} \mathrm{~kg} \)
\( \mathrm{r}=1 \mathrm{~m} \)
\( \omega=\frac{2 \pi \mathrm{N}}{60}=\frac{2 \pi(10)}{60}=\frac{\pi}{3} \mathrm{rad} / \mathrm{sec} \)
\( \mathrm{T}-\mathrm{mg}=\mathrm{mr} \omega^2 \)
\( \mathrm{~T}=\mathrm{mg}+\mathrm{mr} \omega^2 \)
\( =\frac{9}{10} \times 9.8+\frac{9}{10} \times 1\left(\frac{\pi}{3}\right)^2 \)
\( =8.82+\frac{9}{10} \times \frac{\pi^2}{9} \)
\( =8.82+0.98 \)
\( =9.80 \mathrm{~N}\)
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