Motion in a Pla...

A long horizontal rod has a bead which can slide along its length, and initially placed at a distance L from one end A of the rod. The rod is set in angular motion about A with constant angular acceleration α. If the coefficient of friction between the rod and the bead is μ, and gravity is neglected, then the time after which the bead starts slipping is

A small block is shot into each of the four tracks as shown below. Each of the tracks rises to the same height. The speed with which the block enters the track is the same in all cases. At the highest point of the track, the normal reaction is maximum in

The angular amplitude of a simple pendulum is θ₀. The maximum tension in its string will be

A bob of mass M is suspended by a massless string of length L. The horizontal velocity V at position A is just sufficient to make it reach the point B. The angle θ at which the speed of the bob is half of that at A, satisifes

Four persons K, L, M and N are initially at the corners of a square of length d. If every person starts moving such that K is always headed towards L, L towards M, M is headed directly towards N and N towards K, then the four persons will meet after

A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of \'P\' is such that it sweeps out a length s = t³ + 5, where s is in metres and t is in seconds. The radius of the path is 20 m. The acceleration of \'P\' when t = 2s is nearly

A piece of wire is bent in the shape of a parabola y = kx² (y - axis vertical) with a bead of mass m on it. the bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the x-axis with a constant acceleration a. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the y - axis is

A small roller coaster starts at point A with a speed u on a curved track as shown in the figure. The friction between the roller coaster and the track is negligible and it always remains in contact with the track.. The speed of roller coaster at point D on the track will be