#### Question

A stone of mass 100 g attached to a string of length 50 cm is whirled in a vertical circle by giving velocity at lowest point as 7 m/s. Find the velocity at the highest point. [Acceleration due to gravity = 9.8 m/s2 ]

#### Solution

Given:- m = 100 g = 0.1 kg, r = 50 cm = 0.5m, g = 9.8 m/s^{2}, v_{L} = 7 m/s

To find:- Velocity at the highest point (v_{H})

Formula:- `v_H=sqrt((2(TE_(H)))/m-4gr)`

Calculation:- Total energy at highest point,

T.E.(H)= K.E. at lowest point = (1/2)mv_{L}^{2}

∴ T.E_{(H)} = (1/2)x0.1x7^{2}

=2.45 J

From formula,

`v_H=sqrt((2(2.45))/0.1-(4xx9.8xx0.5)`

`=sqrt(29.4)`

`therefore v_H=5.422` m/s

**The velocity at the highest point is 5.422 m/s.**

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#### APPEARS IN

Solution Find the Velocity at the Highest Point. Concept: Acceleration Due to Gravity and Its Variation with Altitude and Depth.