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 .

A car goes on a horizontal circular road of radius R , the speed increasing at a constant rate d v d t = a . The friction coefficient between the road and the tyre is μ . Find the speed at which the car will skid.

When a particle is in a circular motion, two types of accelerations act on the body . a c = centripetal acceleration and a t = tangential acceleration. Now, net acceleration a R = a c 2 + a t 2 , where, a c = v 2 R and a t = d v d t . From F B D , f = m a R , where f = Friction acting on the car. and f = μ N , where, μ = coefficient of friction and N = normal force. Therefore, μ N = m v 2 R 2 + d v d t 2 . Squaring both sides, μ 2 N 2 = m 2 v 4 R 2 + a 2 … ( 1 ) and N = m g … ( 2 ) . Solving equations (1) and (2), v = μ 2 g 2 - a 2 R 2 1 4 .

HARD

JEE Main

IMPORTANT

Earn 100

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 $g = 10 m s^{- 2}$ .

Important Questions on Circular Motion

MEDIUM

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.

MEDIUM

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

MEDIUM

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 17

A person stands on a spring balance at the equator.

(a) By what fraction is the balance reading less than his true weight?

(b) If the speed of Earth's rotation is increased by such an amount that the balance reading is half the true weight, what will be the length of the day in this case?

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?

HARD

JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 7 - Circular Motion>EXERCISES>Q 20

A car goes on a horizontal circular road of radius

R,

the speed increasing at a constant rate

\frac{d v}{d t} = a .

The friction coefficient between the road and the tyre is

μ .

Find the speed at which the car will skid.

HARD

JEE Main

IMPORTANT

CONCEPTS OF PHYSICS [VOLUME 1]>Chapter 7 - Circular Motion>EXERCISES>Q 21

A block of mass $m$ is kept on a horizontal ruler. The friction coefficient between the ruler and the block is $μ .$ The ruler is fixed at one end and the block is at a distance $L$ from the fixed end. The ruler is rotated about the fixed end in the horizontal plane through the fixed end.

(a) What can the maximum angular speed be for which the block does not slip?

(b) If the angular speed of the ruler is uniformly increased from zero at an angular acceleration $α,$ at what angular speed will the block slip?

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.

Important Questions on Circular Motion

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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 $g = 10 m s^{- 2}$ .