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Chapter 8: Q. 59 (page 202)

A 100 g ball on a 60-cm-long string is swung in a vertical circle about a point 200 cm above the floor. The string suddenly breaks when it is parallel to the ground and the ball is moving
upward. The ball reaches a height 600 cm above the floor. What was the tension in the string an instant before it broke?

Short Answer

Expert verified

The tension in the string an instant before it broke was 13 N

Step by step solution

01

Given information

Length of string =60 cm =0.6 m
Mass of ball =100 gm = 0.1 kg
Height it reaches above the ground after breaking= 600 cm = 6 m

02

Explanation

First draw the free body diagram as below

The figure shows forces in a circular motion,

Tension =T, centripetal force = mv2/r and gravitational force = mg.

At the Point, ball move upward,

T=mv2r

Now find velocity of the ball at the breaking point.

v2 = u2 +2as

Where v=0, u=v and a=g, and s=600-200=400cm=4 m

On substitution we get

0 =v2 -2 x g x4m

v2 = (8m) g = (8m )x (9.8 m/s2)

Use this and substitute given values to calculate tension

T=mv2r=(0.1kg)(8m脳9.8m/s2)0.6m=13N

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