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Byju's Answer

Standard XII

Physics

Law of Conservation of Mechanical Energy

A stone of ma...

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 point of the circle directed vertically downwards are
$T_{1}$ and $v_{1}$ denotes the tension and speed at the lowest point. $T_{2}$ and $v_{2}$ denotes corresponding values at the highest point.

Lowest Point

m g - T_{1}

, Highest Point-

m g + T_{2}

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Lowest Point

m g + T_{1}

, Highest Point-

m g - T_{2}

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Lowest Point

m g + T_{1} - (\frac{m v_{1}^{2}}{R})

Highest Point

m g - T_{2} + (\frac{m v_{2}^{2}}{R})

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Lowest Point

m g - T_{1} - (\frac{m v_{1}^{2}}{R})

Highest Point

m g + T_{2} + (\frac{m v_{2}^{2}}{R})

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Solution

The correct option is A Lowest Point $m g - T_{1}$ , Highest Point- $m g + T_{2}$
At the lowest point, both mg and $T_{2}$ act downwards and $T_{1}$ upwards so that net force = $m g - T_{1}$ .
At heights point, both mg and $T_{2}$ act downwards so that net force = $m g + T_{2}$ .
Hence option (A) is correct.

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Similar questions

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.

	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

Q. A simple pendulum of mass m is performing vertical circular motion with its velocity at the highest point being V

= \sqrt{2 g l}

where l is the length of the string. Find the tension in the string when it reaches the lowest point.

A body moves in a vertical semicircle of radius r from the lowest point to highest point. What is the amount of work done? (Assume mass of the body to be 'm' kg and acceleration due to gravity to be $g m s^{- 2}$ )

Q. A mass

m

is revolving in a vertical circle at the end of a string of length

20 cms

. By how much does the tension of the string at the lowest point exceed the tension at the topmost point

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The correct option is A Lowest Point mg−T1, Highest Point- mg+T2At the lowest point, both mg and T2 act downwards and T1 upwards so that net force = mg−T1.At heights point, both mg and T2 act downwards so that net force = mg+T2.Hence option (A) is correct.