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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.

Important Questions on Circular Motion

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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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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.
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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?
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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].
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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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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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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.
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Alpha Question Bank for Engineering: Physics>Chapter 7 - Circular Motion>Exercise - 1>Q 26
A circular road of radius 1000 m has a banking angle 45°. Find the maximum safe speed of a car having mass 2000 kg, if the coefficient of friction between tyre and road is 0.5.