Q. 264.7( 7 Votes )

# 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]

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.

Answer :

Given:

Mass of body = m Kg

Radius of vertical circle = R m

From the free body diagram of body at lowest point, we can write,

According Newton’s 2^{nd} law of motion,

F_{net} = mg-T

F_{net} = mv_{1}^{2}/R (Centrifugal force)

mg-T = mv_{1}^{2}/R …(1)

Where,

v_{1} = Velocity at lowest point.

m = mass of body

R = radius of path

T = tension in string

From the free body diagram of body at highest point , we can write,

F_{net} = T + mg

F_{net} = mv_{2}^{2}/ R

Where,

v_{2} = velocity of body at highest point,

T + mg = mv_{2}^{2}/ R …(2)

From equation (1) and (2) we conclude that option (1) is correct.

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