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]

Lower Point Highest Point
a. mg - $T_{1}$ mg + $T_{2}$
b. mg + $T_{1}$ mg - $T_{2}$
c. mg + $T_{1} - (m v_{1}^{2}) / R$ mg - $T + (m v_{1}^{2}) / R$
d. mg - $T_{1} - (m v_{1}^{2}) / R$ mg + $T_{2} + (m v_{1}^{2}) / R$
$T_{1}$ and $v_{1}$ denote the tension and speed at the lowest point. $T_{2}$ and $v_{2}$ denote corresponding values at the highest point

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Solution

In the given figure shown here $L$ and $H$ show the lowest and highest point respectively.
At point L: $T_{1}$ acts towards the centre of the circle and $m g$ acts vertically downwards.
Now net force on the stone at the lowest point in the downward direction $= m g - T_{1}$
At the point : Both $T_{2}$ and $m g$ act vertically downward towards the centre of the vertical circle.
Again the net force on the stone at the highest point in the downward direction $= T_{2} + m g$
Hence option (a) is the correct alternative.

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Q. 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] Lowest Point Highest Point (a) mg – T₁ mg + T₂ (b) mg + T₁ mg – T₂ (c) mg + T₁ – (m v ²₁ ) / R mg – T₂ + (m v ²₁ ) / R (d) mg – T₁ – (m v ²₁ ) / R mg + T₂ + (m v ²₁ ) / R T₁ and v₁ denote the tension and speed at the lowest point. T₂ and v₂ denote corresponding values at the highest point.

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]

	Lowest Point	Highest Point
(a)	mg – T₁	mg + T₂
(b)	mg + T₁	mg – T₂
(c)	mg + T₁ –/R	mg – T₂ + /R
(d)	mg – T₁ – /R	mg + T₂ + /R

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30^{\circ}

and

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from vertical (lowest position) are

T_{1}

and

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respectively. Then

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	Lower Point	Highest Point
a.	mg - $T_{1}$	mg + $T_{2}$
b.	mg + $T_{1}$	mg - $T_{2}$
c.	mg + $T_{1} - (m v_{1}^{2}) / R$	mg - $T + (m v_{1}^{2}) / R$
d.	mg - $T_{1} - (m v_{1}^{2}) / R$	mg + $T_{2} + (m v_{1}^{2}) / R$