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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.

Important Questions on Circular Motion

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Alpha Question Bank for Engineering: Physics>Chapter 7 - Circular Motion>Exercise - 1>Q 15
A particle is projected with a speed u at an angle θ with the horizontal. Find the radius of curvature of the parabola traced out by the projectile at a point, where the particle velocity makes an angle θ2 with the horizontal.
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Alpha Question Bank for Engineering: Physics>Chapter 7 - Circular Motion>Exercise - 1>Q 16
A weightless thread can support tension up to 30 N. A stone of mass 0.5 kg is tied to it and is revolved in a circular path of radius 2 m in a vertical plane. If g=10 m s-2, find the maximum angular velocity of the stone.
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Alpha Question Bank for Engineering: Physics>Chapter 7 - Circular Motion>Exercise - 1>Q 17
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?
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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 ABCDE 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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IMPORTANT
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 μ2, what is the maximum speed permitted?
EASY
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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].