A stone of mass 900 g is tied to a string and moved in a vertical circle of radius 1 m, making 10 rpm. The tension in the string when the stone is at the lowest point is (if = 9.8 and g = 9.8 )

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Solution

Q.
A stone of mass 900 g is tied to a string and moved in a vertical circle of radius 1 m, making 10 rpm. The tension in the string when the stone is at the lowest point is (if $π^{2}$ = 9.8 and g = 9.8 $m / s^{2}$ ) [2024]

1 17.8 N

2 8.82 N

3 97 N

4 9.8 N

Ans.
(4)

Given that, $m = 900 gm = \frac{900}{1000} kg = \frac{9}{10} kg$

$r = 1 m$

$ω = \frac{2 π N}{60} = \frac{2 π (10)}{60} = \frac{π}{3} rad/sec$

$T - m g = m r ω^{2} \Rightarrow T = m g + m r ω^{2}$

$\Rightarrow T = \frac{9}{10} \times 9.8 + \frac{9}{10} \times 1 {(\frac{π}{3})}^{2}$

$= 8.82 + \frac{9}{10} \times \frac{π^{2}}{9} = 9.80 N$

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