Suppose the amplitude of a simple pendulum having a bob of mass m is θ 0 . Find the tension in the string when the bob is at its extreme position.

Given, mass of bob = m , amplitude of simple pendulum = θ 0 . FBD of bob Net force towards the centre will provide the centripetal force. Net force towards centre = T - m g cosθ 0 … ( 1 ) At extreme position, F C = centripetal force = 0 … ( 2 ) From equations ( 1 ) and ( 2 ) , T = m g cos θ 0 .

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JEE Main

IMPORTANT

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A stone is fastened to one end of a string and is whirled in a vertical circle of radius $R$ . Find the minimum speed the stone can have at the highest point of the circle.

Important Questions on Circular Motion

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JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 7 - Circular Motion>EXERCISES>Q 11

A ceiling fan has a diameter (of the circle through the outer edges of the three blades) of $120 cm$ and $rpm 1500$ at full speed. Consider a particle of mass $1 g$ sticking at the outer end of a blade.

(a) How much force does it experience when the fan runs at full speed?

(b) Who exerts this force on the particle?
(c) How much force does the particle exert on the blade along its surface?

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JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 7 - Circular Motion>EXERCISES>Q 12

A mosquito is sitting on an L.P. record disc rotating on a turntable at

33 \frac{1}{3}

revolutions per minute. The distance of the mosquito from the centre of the turntable is

10 cm

. Show that the friction coefficient between the record and the mosquito is greater than

\frac{π^{2}}{81}

. Take,

g = 10 m s^{- 2}

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JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 7 - Circular Motion>EXERCISES>Q 13

A simple pendulum is suspended from the ceiling of a car taking a turn of radius

10 m

at a speed of

36 km h^{- 1}

. Find the angle made by the string of the pendulum with the vertical if this angle does not change during the turn. Take

g = 10 m s^{- 2}

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JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 7 - Circular Motion>EXERCISES>Q 14

The bob of a simple pendulum of length

1 m

has mass

100 g

and a speed of

1.4 m s^{- 1}

at the lowest point in its path. Find the tension in the string at this instant.

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JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 7 - Circular Motion>EXERCISES>Q 15

Suppose, the bob of the previous problem has a speed of

1.4 m s^{- 1}

when the string makes an angle of

0.20 rad

with the vertical. Find the tension at this instant. You can use

\cos θ = 1 - \frac{θ^{2}}{2}

and

\sin θ = θ

for small

θ

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JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 7 - Circular Motion>EXERCISES>Q 16

Suppose the amplitude of a simple pendulum having a bob of mass

m

θ_{0}

. Find the tension in the string when the bob is at its extreme position.

HARD

JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 7 - Circular Motion>EXERCISES>Q 18

A turn of radius

20 m

is banked for the vehicles going at a speed of

36 km h^{- 1}

. If the coefficient of static friction between the road and the tyre is

0.4

, what are the possible speeds of a vehicle, so that it neither slips down nor skids up?

HARD

JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 7 - Circular Motion>EXERCISES>Q 19

A motorcycle has to move with a constant speed on an overbridge which is in the form of a circular arc of radius $R$ and has a total length $L$ . Suppose the motorcycle starts from the highest point.
(a) What can its maximum velocity be for which the contact with the road is not broken at the highest point?
(b) If the motorcycle goes at speed $\frac{1}{\sqrt{2}}$ times the maximum found in part $(a)$ where will it lose the contact with the road?
(c) What maximum uniform speed can it maintain on the bridge if it does not lose contact anywhere on the bridge?

A stone is fastened to one end of a string and is whirled in a vertical circle of radius R. Find the minimum speed the stone can have at the highest point of the circle.

Important Questions on Circular Motion

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A stone is fastened to one end of a string and is whirled in a vertical circle of radius $R$ . Find the minimum speed the stone can have at the highest point of the circle.