Ncert Exercises & Solutions

5.26 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 : [Choose the correct alternative]

$L o w e s t P o i n t H i g h e s t P o i n t$
$(a) m g - T_{1} m g + T_{2}$
$(b) m g + T_{1} m g - T_{2}$
$(c) m g + T_{1} - (m {v_{1}}^{2}) / R m g - T_{2} + (m {v_{2}}^{2}) / R$
$(d) m g - T_{1} - (m {v_{1}}^{2}) / R m g + T_{2} + (m {v_{2}}^{2}) / R$

T1 and v1 denote the tension and speed at the lowest point. T2 and v2 denote corresponding values at the highest point.

In the figure shown here, L and H show the lowest and highest points respectively.
At point L:

T₁ acts towards the center of the circle and mg acts vertically downward.
So, Net force on the stone at the lowest point in the downward direction = $T_{1} - m g = \frac{m {v_{1}}^{2}}{R}$
At point H:

Both T₂ and mg act vertically downward towards the center of the vertical circle.
So, Net force on the stone at the highest point in the downward direction = $T_{2} + m g = \frac{m {v_{2}}^{2}}{R}$ So option (a) is the correct alternative.

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