Question 57: Work, Energy and Power & Circular Motion

Question

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 $$g=9.8 \mathrm{~m} / \mathrm{s}^2$$) :

Accepted Answer

Given that
$$\begin{aligned}
& \mathrm{m}=900 \mathrm{~gm}=\frac{900}{1000} \mathrm{~kg}=\frac{9}{10} \mathrm{~kg} \
& \mathrm{r}=1 \mathrm{~m} \
& \omega=\frac{2 \pi \mathrm{N}}{60}=\frac{2 \pi(10)}{60}=\frac{\pi}{3} \mathrm{rad} / \mathrm{sec} \
& \mathrm{T}-\mathrm{mg}=\mathrm{mr} \omega^2 \
& \mathrm{~T}=\mathrm{mg}+\mathrm{mr} \omega^2 \
& =\frac{9}{10} 	imes 9.8+\frac{9}{10} 	imes 1\left(\frac{\pi}{3}ight)^2 \
& =8.82+\frac{9}{10} 	imes \frac{\pi^2}{9} \
& =8.82+0.98 \
& =9.80 \mathrm{~N}
\end{aligned}$$

Answer

17.8 N

Answer

97 N

Answer

9.8 N

Answer

8.82 N

Work, Energy and Power & Circular Motion

A stone of mass $900 \mathrm{~g} is tied to a string and moved in a vertical circle of radius 1 \mathrm{~m} making 10 \mathrm{~rpm}. The tension in the string, when the stone is at the lowest point is (if \pi^2=9.8 and g=9.8 \mathrm{~m} / \mathrm{s}^2$) :

Choose the correct answer: