A stone of mass m tied to the end of a string revolves in a vertical circle of radius R. The net forces at the lowest and highest points of the circle directed vertically downwards are

Question

A stone of mass $m$ tied to the end of a string revolves in a vertical circle of radius $R$ . The net forces at the lowest and highest points of the circle directed vertically downwards are

$T_{1}$ and $v_{1}$ denote the tension and speed at the lowest point. $T_{2}$ and $v_{2}$ denote corresponding values at the highest point.

Smart Achievers · Accepted Answer

(1)

At the lowest point, $R$ acts downwards and $T_{1}$ upwards so that net force $v_{1}$ .

At the highest point, both $m g$ and $T_{2}$ act downwards so that net force $= m g + T_{2}$ .

Hence, option (1) is correct.

Solution

1 Lowest Point: $m g - T_{1}$ Highest Point: $m g + T_{2}$

2 Lowest Point: $m g + T_{1}$ Highest Point: $m g - T_{2}$

3 Lowest Point: $m g + T_{1} - (\frac{m v_{1}^{2}}{R})$ Highest Point: $m g - T_{2} + (\frac{m v_{2}^{2}}{R})$

4 Lowest Point: $m g - T_{1} - (\frac{m v_{1}^{2}}{R})$ Highest Point: $m g + T_{2} + (\frac{m v_{2}^{2}}{R})$

Ans.
(1)

At the lowest point, $m g$ acts downwards and $T_{1}$ upwards so that net force $= m g - T_{1}$ .

At the highest point, both $m g$ and $T_{2}$ act downwards so that net force $= m g + T_{2}$ .

Hence, option (1) is correct.

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Solution

1 Lowest Point: mg-T1 Highest Point: mg+T2

2 Lowest Point: mg+T1 Highest Point: mg-T2

3 Lowest Point: mg+T1-(mv12R) Highest Point: mg-T2+(mv22R)

4 Lowest Point: mg-T1-(mv12R) Highest Point: mg+T2+(mv22R)