A body tied to a string of length L is revolved in a vertical circle with minimum velocity, when bod

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7.Gravitation

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A body tied to a string of length $L$ is revolved in a vertical circle with minimum velocity, when the body reaches the upper most point the string breaks and the body moves under the influence of the gravitational field of earth along a parabolic path. The horizontal range $AC$ of the body will be

A

$x = L$

B

$x = 2L$

C

$x = 2\sqrt {2L}$

D

$x = \sqrt {2L}$

Solution

For looping the loop minimum velocity at top

point $v=\sqrt{g L}$

time taken by particle

$t=\sqrt{\frac{2 h}{g}}=\sqrt{\frac{2 \times 2 L}{g}}=2 \sqrt{\frac{L}{g}}$

$\text { horizontal range } x=v t=\sqrt{g L} \times 2 \sqrt{\frac{L}{g}}=2 L$

Standard 11

Physics

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