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Question

A ball of mass 100 g is suspended a string 40 cm long. Keeping the string taut , the ball describes a horizontal circle of radius 10 cm Find the angular speed.

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Solution

Given that,

Mass m=100g

Length l=40cm

Radius r=10cm

Now, by force equilibrium equation in vertical direction

FTcosθ=mg.....(I)

By horizontal direction force equation

FTsinθ=mω2r....(II)

Now, the ratio of above equations

tanθ=ω2rg....(III)

We know that,

sinθ=14

θ=14.47

θ=14.5

Now, from equation (III)

tanθ=ω2rg

ω=gtanθr

ω=10×tan14.510

ω=4.949

ω=5.1rad/s

Hence, the angular speed is 5.1 rad/s


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