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Friction and Vertical Circular Motion Problems

A body of mas...

Question

A body of mass m is rotated at uniform speed along a vertical circle with the help of light string. If $T_{1} a n d T_{2}$ are tensions in the string when the body is crossing highest and lowest point of the vertical circle respectively, then which of the following expressions is correct?

A

T_{2} - T_{1} = 6 m g

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B

T_{2} - T_{1} = 4 m g

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C

T_{2} - T_{1} = 2 m g

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D

T_{2} - T_{1} = m g

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Solution

The correct option is C $T_{2} - T_{1} = 2 m g$
Centripetal Force is: $\frac{m v^{2}}{r}$
At the highest point: $T_{1} = \frac{m v^{2}}{r} - m g$
At the lowest point: $T_{2} = \frac{m v^{2}}{r} + m g$
$∴ T_{2} - T_{1} = \frac{m v^{2}}{r} + m g - (\frac{m v^{2}}{r} - m g) = 2 m g$

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Q. A body of mass m is rotated in a vertical circle with help of light string such that velocity of body at a point is equal to critical velocity at that point. If

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Q. A stone of mass m tied to the end of a string revolves in a vertical circle of radius R.The net forces at the lowest and highest points of the circle directed vertically downwards are : [Choose the correct alternative]

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a.	mg - $T_{1}$	mg + $T_{2}$
b.	mg + $T_{1}$	mg - $T_{2}$
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