MEDIUM
JEE Main/Advance
IMPORTANT
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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.

Important Questions on Circular Motion

EASY
JEE Main/Advance
IMPORTANT
When the road is dry and coefficient of friction is μ, the maximum speed of a car in a circular path is 10 m s1. If the road becomes wet and the coefficient of friction become μ2, what is the maximum speed permitted?
EASY
JEE Main/Advance
IMPORTANT
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
JEE Main/Advance
IMPORTANT
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)
MEDIUM
JEE Main/Advance
IMPORTANT
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:
MEDIUM
JEE Main/Advance
IMPORTANT
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.
EASY
JEE Main/Advance
IMPORTANT
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.
MEDIUM
JEE Main/Advance
IMPORTANT

In the figure shown a lift goes downwards with constant retardation. An observer in the lift observers a conical pendulum in the lift, revolving in a horizontal circle with time period 2 seconds. The distance between the centre of the circle and the point of suspension is 2.0 m. Find the retardation of the lift in m s-2. Use π2 = 10 and g=10 m s-2

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HARD
JEE Main/Advance
IMPORTANT
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?