Laws of Motion

Question : 26 of 40

Marks: +1, -0

A stone of mass m tied to the end of a string revolves in a vertical circle of radius R. The net force at the lowest and highest points of the circle directed vertically downwards are : [Choose the correct alternative]

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

T_1 \text{ and } v_1

denote the tension and speed at the lowest point.

T_2 \text{ and } v_2

denotecorresponding values at the highest point

Solution:

In the figure shown here L and H shows the lowest and highest points respectively.

At point L :

T_1

acts towards the centre of the circle and mg acts vertically downward.

∴ Net force on the stone at the lowest point in the downward direction

= m g - T_1

At point H : Both

T_2

and mg act vertically downward towards the centre of the vertical circle.

∴ Net force on the stone at the highest point in the downward direction

= T_2 + m g

So option (a) is the correct alternative.

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