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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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Similar questions

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

T_{1}, T_{2}

be the tensions in the string when the body is crossing the highest and the lowest points of vertical circle respectively, then which of the following relation is correct?

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]

	Lower Point	Highest Point
a.	mg - $T_{1}$	mg + $T_{2}$
b.	mg + $T_{1}$	mg - $T_{2}$
c.	mg + $T_{1} - (m v_{1}^{2}) / R$	mg - $T + (m v_{1}^{2}) / R$
d.	mg - $T_{1} - (m v_{1}^{2}) / R$	mg + $T_{2} + (m v_{1}^{2}) / R$

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v_{1}

denote the tension and speed at the lowest point.

T_{2}

v_{2}

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Q. A particle is moving in a vertical circle. The tensions in the string when passing through two positions at angles

30^{\circ}

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T_{1}

T_{2}

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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] Lowest Point Highest Point (a) mg – T₁ mg + T₂ (b) mg + T₁ mg – T₂ (c) mg + T₁ – (m v ²₁ ) / R mg – T₂ + (m v ²₁ ) / R (d) mg – T₁ – (m v ²₁ ) / R mg + T₂ + (m v ²₁ ) / R T₁ and v₁ denote the tension and speed at the lowest point. T₂ and v₂ denote corresponding values at the highest point.

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