A motorcyclist wants to drive on the vertical surface of a wooden ‘well’ of radius 5 m , in a horizontal plane with the speed of 5 5 m s - 1 . Find the minimum value of the coefficient of friction between the tyres and the wall of the well. (take g = 10 m s - 2 )

The friction force between the wall and the tyres balances the weight of motorcyclist during the motion on wall in horizontal plane. According to question, r = 5 m , v = 5 5 m s - 1 and g = 10 m s - 2 . ⇒ μ N = m g . . . 1 , where μ is coefficient of friction, N is normal reaction by motorcyclist on wall and m is mass of motorcyclist. The normal reaction on the wall provides the necessary centripetal force for circular motion, therefore, N = m v 2 r . . . 2 From 1 and 2 , we get ⇒ μ m v 2 r = m g ⇒ μ = r g v 2 = 5 10 5 5 2 = 0 . 4

EASY

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IMPORTANT

Earn 100

A particle moves uniformly in a circle of radius $25 cm$ at two revolution per second. Find the acceleration of the particle in $m s^{- 2}$ .

Important Questions on Circular Motion

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JEE Main/Advance

IMPORTANT

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

A car is moving with speed

30 m \sec^{- 1}

on a circular path of radius

500 m

. Its speed is increasing at the rate of

2 m \sec^{- 2}

. What is the acceleration of the car at that moment?

MEDIUM

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IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 7 - Circular Motion>Exercise - 1>Q 8

A particle moves in a circle of radius $1.0 cm$ at a speed given by $v = 2.0 t$ where $v$ is in $cm s^{- 1}$ and $t$ in seconds.

(a) Find the radial acceleration of the particle at $t = 1 s$ .

(b) Find the tangential acceleration at $t = 1 s$ .

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Alpha Question Bank for Engineering: Physics>Chapter 7 - Circular Motion>Exercise - 1>Q 9

A particle is moving along a circular path of radius

5 m

with a uniform speed

5 m s^{- 1}

. What is the magnitude of average acceleration during the interval in which the particle completes half revolution?

HARD

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IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 7 - Circular Motion>Exercise - 1>Q 10

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}

MEDIUM

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IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 7 - Circular Motion>Exercise - 1>Q 11

A motorcyclist wants to drive on the vertical surface of a wooden ‘well’ of radius

5 m

, in a horizontal plane with the speed of

5 \sqrt{5} m s^{- 1}

. Find the minimum value of the coefficient of friction between the tyres and the wall of the well. (take

g = 10 m s^{- 2}

)

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 7 - Circular Motion>Exercise - 1>Q 12

A mass is kept on a horizontal frictionless surface. It is attached to a string and rotates about a fixed centre at an angular velocity

ω_{0}

. If the length of the string and angular velocity is doubled, find the tension in the string which was initially

T_{0}

MEDIUM

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IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 7 - Circular Motion>Exercise - 1>Q 13

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. What is the net force on it, when the fan runs at full speed? Who exerts this force on the particle? How much force does the particle exert on the blade in the plane of motion?

MEDIUM

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IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 7 - Circular Motion>Exercise - 1>Q 14

A ball is projected with initial speed

u

and making an angle

θ

with the vertical. Consider a small part of the trajectory near the highest position and take it approximately to be a circular arc. What is the radius of this circle? This radius is called the radius of curvature of the curve at the point.

A particle moves uniformly in a circle of radius 25 cm at two revolution per second. Find the acceleration of the particle in m s-2 .

Important Questions on Circular Motion

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A particle moves uniformly in a circle of radius $25 cm$ at two revolution per second. Find the acceleration of the particle in $m s^{- 2}$ .