Question

a A small stone of mass 200 g, connected with an ideal string, is rotated in a vertical circle of radius 50 cm. Minimum speed needed at the lowest point for looping the loop will
a) 10 ms^-1
b) 5 ms^-1
c) 6 ms^-1
c) 5√10 m s^-1​

Answer 1

Given:

A small stone of mass 200 g, connected with an ideal string, is rotated in a vertical circle of radius 50 cm.

To find:

Minimum speed needed at lowest point ?

Calculation:

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The minimum speed needed for completion of a vertical circular track is:

$\sf \: v_{min} = \sqrt{5gr}$

• 'g' is gravitational acceleration and 'r' is radius of circular track.

$\sf \implies\: v_{min} = \sqrt{5 \times 10 \times \dfrac{50}{100} }$

$\sf \implies\: v_{min} = \sqrt{ \dfrac{2500}{100} }$

$\sf \implies\: v_{min} = \sqrt{ 25}$

$\sf \implies\: v_{min} = 5 \: m/s$

So, minimum velocity needed is 5 m/s