Question

Q. A stone tied to a string of length l is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest point and has a speed u. Then what is the magnitude of change in velocity as it reaches its highest point of the circle?​

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Answer 1

Answer:

Given:

Stone is tied to a string of length l and rotated in a vertical circle. Velocity at lowest point = u

To find:

Change in magnitude of velocity when it reaches the highest point.

Concept:

In a vertical circle , we shall consider Conservation Of Mechanical Energy concept.

The sum of initial Kinetic and Potential Energy shall be equal to Final Kinetic and potential energy sum.

Calculation:

∴ KE1 + PE1 = KE2 + PE2

$= > \frac{1}{2} m {u}^{2} + 0 = \frac{1}{2} m {v}^{2} + mg(2l)$

Cancelling the similar terms :

$= > \dfrac{ {u}^{2} }{2} = \dfrac{ {v}^{2} }{2} + 2gl$

$= > {u}^{2} = {v}^{2} + 4gl$

$= > {v}^{2} = {u}^{2} - 4gl$

$= > v = \sqrt{ {u}^{2} - 4gl }$

Now the difference in magnitude of velocities shall be :

$\Delta |v| = |v| - |u|$

$= > \Delta |v| = \sqrt{ {u}^{2} - 4gl} - u$