Motion in a Pla...

A particular P is moving in a circle of radius ‘r’ with a uniform speed v. C is the centre of the circle and AB is the diameter. The angular velocity of P about A and C is in ratio

A body slides down a frictionless track which ends in a circular loop of diameter D. Then the minimum height h of the body in terms of D so that it may just complete the loop, is

A wheel is subjected to uniform angular acceleration about its axis. Initially, its angular velocity is zero. In the first two seconds, it rotates through angle θ₁, and in the next two seconds, it rotates through angle θ₂. Then θ₂/θ₁is

An electric fan has blades of length 30 cm measured from the axis of rotation. If the fan is rotating at 120 rpm, the acceleration of a point on the tip of the blade is

A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/sec. A plumb bob is suspended from the roof of the car by a light rigid rod of length 1.00 m. The angle made by the rod with track is

A wheel making 20 revolution per second is stopped in 20 seconds. Its angular retardation is

A boat is sent across a river with a velocity of 8 km h^-1. If the resultant velocity of boat is 10 km h^-1, then velocity of river is

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration a_c is varying with time t a_c = k²rt², where k is a constant. The power delivered to the particle by the forces acting on it is

A particle reaches its highest point when it has covered exactly one half of its horizontal range. The corresponding point on the displacement - time graph is characterised by