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Important Questions: Dynamics of uniform circular motion, centripetal force and its applications: vehicle on a level circular road, vehicle on a banked road for JEE

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Q1PhysicsUnit 3: Laws of Motion
A circular road of radius r is banked for a speed v=40km/hr.\mathbf{v}=40 \mathrm{km} / \mathrm{hr} . A car of mass m\mathrm{m} attempts to go on the circular road. The friction coefficient between the tyre and the road is negligible.
Q2PhysicsUnit 3: Laws of Motion
A body is revolving with a constant speed along a circular path. If the direction of its velocity is reserved, keeping speed unchanged, then at that instant.
Q3PhysicsUnit 3: Laws of Motion
If the angle of banking of a road is 3232^{\circ} and if a turn has radius 72m,72 m, what is the maximum speed at which a car can turn, given the coefficient of friction between the car tyres and the road is 0.34?(inm/s)\mathbf{0 . 3 4} ?(\operatorname{in} \mathbf{m} / \mathbf{s})
Q4PhysicsUnit 3: Laws of Motion
A ball of mass 2kg2 k g is connected to a string of length 1m1 m and made to move in a horizontal circle on a smooth frictionless table with a constant speed of 2m/s.2 m / s . The other end of the string is connected to a fixed peg on the table. Find the magnitude of the average impulse exerted by the string on the ball in half a revolution:
Q5PhysicsUnit 3: Laws of Motion
Q Type your question the shape of track is defined by equation y=x2ay=\frac{x^{2}}{a} where aa is a constant. A ring of mass mm which can slide freely on wire track, is placed at the position (a,a).(a, a) . The track is rotated with constant angular speed ω\omega such that there is no relative slipping between the ring and the track then ω\omega is equal to
Q6PhysicsUnit 3: Laws of Motion
The distance between two rails of railway track is 1.6m1.6 \mathrm{m} along a curve of radius 800m.800 \mathrm{m} . The outer rail is raised above the inner rail by 10cm.10 \mathrm{cm} . With what maximum speed can a train be safely driven along the curve

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