A motorcycle has to move with a consatnt speed on an overbridge which is in the form of as circular arc of radius R and has a total length L. Suppose the motorcycle starts from the highest point. a) what can its maximum velocity be for which the contact with the road is not broken at the highest point? b) If the motorcycle goes at speed 1/sqrt2 times the maximum found in part a. where will it lose the contact with the road? c) What maximum uniform speed can it maintain on the bridge if it does not lose contact anywhere on the bridge?

The angular velocity of the engine (and hence of the wheel) on a scooter is proportional to the petrol input per second. The scooter is moving on a frictionless road with uniform velocity. If the petrol input is increased by 10% the linear velocity of the scooter is increased by

A plumb bob is hung from the ceiling of a train compartment. If the train moves with an acceleration a along a straight horizontal track, the string supporting the bob makes an angle tan^1 (a/g) with the normal to the ceiling. Suppose the train moves on an inclined straight track with uniform velocity, if the angle of incline is tan^-1(a/g) , the string again makes the same angle with the normal to the ceiling. Can a person sitting inside the compartment tell by looking at the plumb line whether the train is accelerated on a horizontal straight track or it is going on an incline? If yes, how? If no, suggest a method to do so.

A conducting wire ab of length l, resistance r and mass m starts sliding at t = 0 down a smooth, vertical, thick pair of connected rails as shown in . A uniform magnetic field B exists in the space in a diraction perpendicular to the plane of the rails. (a) Write the induced emf in the loop at an instant t when the speed of the wire is v. (b) what would be the magnitude and direction of the induced current in the wire? (c) Find the downward acceleration of the wire at this instant. (d) After sufficient time, the wire starts moving with a constant velocity. Find this velocity v_m. (e) Find the velocity of the wire as a function of time. (f) Find the displacement of the wire as a functong of time. (g) Show that the rate of heat developed inte wire is equal to the rate at which the gravitational potential energy is decreased after steady state is reached.

Can you accelerate a car on a frictionless horizontal road by putting more petrol in the engine? Can you stop a car going on a frictionless horizontal road by applying brakes?

In rear wheel drive cars the engine rotastes the rear whel and the front wheels rotates only becomes the car moves. Ilf such a car accelerates on horizontal road the friction

Consider the situation shown in . The wire PQ has mass m, resistance r and can slide on the smooth, horizontal parallel rails separted by a distance l. The resistance of the rails is negligible. A uniform magnetic field B exists in the rectangualr region and a resistance R connects the rails outsided the field region At t= 0, the wire PQ is puched towards right with a speed v_0 . find (a) the current in the loop at an instant when the speed of the wire PQ is v, (b) the acceleration of the wire at this instatn, (c ) the velocity v as a function of x and (d) the maximum distance the wire will move.