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A simple pendulum oscillates in a vertical plane. When it passes through the mean position, the tension in the string is $3$ times the weight of the pendulum bob. What is the maximum angular displacement of the pendulum of the string with respect to the downward vertical?

Important Questions on Circular Motion

HARD

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IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 7 - Circular Motion>Exercise - 1>Q 18

A small body of mass

m

hangs at one end of a string of length

a

, the other end of which is fixed. It is given a horizontal velocity

u

at its lowest position so that the string would just become slack when it makes an angle of

60 °

with the upward drawn vertical line. Find the tension in the string at the point of projection.

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Alpha Question Bank for Engineering: Physics>Chapter 7 - Circular Motion>Exercise - 1>Q 19

A frictionless track $A B C D E$ ends in a circular loop of radius $R$ . A body slides down the track from point A which is at height $h = 5 cm$ . Find the maximum value of $R$ for a body to complete the loop successfully.

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Alpha Question Bank for Engineering: Physics>Chapter 7 - Circular Motion>Exercise - 1>Q 20

A body attached to a string of length

l

describes a vertical circle such that it is just able to cross the highest point. Find the minimum velocity at the bottom of the circle.

EASY

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Alpha Question Bank for Engineering: Physics>Chapter 7 - Circular Motion>Exercise - 1>Q 21

When the road is dry and coefficient of friction is

μ

, the maximum speed of a car in a circular path is

10 m s^{- 1}

. If the road becomes wet and the coefficient of friction become

\frac{μ}{2}

, what is the maximum speed permitted?

EASY

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IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 7 - Circular Motion>Exercise - 1>Q 22

Find the maximum speed at which a car can turn round a curve of

30 m

radius on a level road if the coefficient of friction between the tyres and the road is

0.4 [g = 10 m s^{- 2}] .

EASY

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IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 7 - Circular Motion>Exercise - 1>Q 23

A cyclist moving with a speed of

4.9 m s^{- 1}

on a level road can take a sharp circular turn of radius

4 m

, then find the minimum value of the coefficient of friction between the cycle tyres and road.

(g = 9.8 m s^{- 2})

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IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 7 - Circular Motion>Exercise - 1>Q 24

A train has to negotiate a curve of radius

400 m

. By how much height should the outer rail be raised with respect to the inner rail for a speed of

48 km {hr}^{- 1}

? The distance between the rails is

1 m

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IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 7 - Circular Motion>Exercise - 1>Q 25

A road surrounds a circular playing field having a radius of

10 m

. If a vehicle goes around it at an average speed of

18 km {hr}^{- 1}

, find proper angle of banking for the road. If the road is horizontal (no banking), what should be the minimum friction coefficient so that a scooter going at

18 km {hr}^{- 1}

does not skid.

A simple pendulum oscillates in a vertical plane. When it passes through the mean position, the tension in the string is 3 times the weight of the pendulum bob. What is the maximum angular displacement of the pendulum of the string with respect to the downward vertical?

Important Questions on Circular Motion

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A simple pendulum oscillates in a vertical plane. When it passes through the mean position, the tension in the string is $3$ times the weight of the pendulum bob. What is the maximum angular displacement of the pendulum of the string with respect to the downward vertical?