Laws Of Motion

A ship of mass kg initially at rest, is pulled by a force of through a distance of 3 m. Assuming that the resistance due to water is negligible, the speed of the ship is

A reference frame attached to the earth

A simple pendulum of length L and mass (bob) M is oscillating in a plane about a vertical line between angular limits- and For an angular displacement , the tension in the string and the velocity of the bob are T and v respectively. The following relations hold good under the above conditions

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

During paddling of a bicycle, the force of friction exerted by the ground on the two wheels is such that it acts

A string of negligible mass going over a clamped pulley of mass supports a block of mass as shown in the figure. The force on the pulley by the clamp is given by

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

Two particles of mass each are tied at the ends of a light string of length . The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance from the centre (as shown in the figure). 

Now, the mid-point of the string is pulled vertically upwards with a small but constant force . As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes is

block of mass is on an inclined plane of angle . The coefficient of friction between the block and the plane is and tan The block is held stationary by applying a force parallel to the plane. The direction of force pointing up the plane is taken to be positive. As is varied from to , the frictional force versus graph will look like

A ball of mass (m) 0.5 kg is attached to the end of a string having length (l) 0.5 m. The ball is rotated on a horizontal circular path about vertical axis. The maximum tension that the string can bear is 324 N. The maximum possible value of angular velocity of ball (in rad/s) is

A solid sphere of mass and radius rolls without slipping on a fixed inclined plane with an angle of inclination from the horizontal .Two forces of magnitude each, parallel to the incline, act on the sphere, both at distance from the center of the sphere, as shown in the figure. The acceleration of the sphere down the plane is ____ (Take )

A person of height 1.6 m is walking away from a lamp post of height 4 m along a straight line on the horizontal ground. The lamp post and the person are always vertical. If the speed of the person is 60 cm/sec, then find the speed of tip point of its shadow with respect to the person in cm/sec.

A particle of mass m is moving such that its velocity at a point (x,y) is given by v = α (y + 2x ), where α is a non-zero constant. What is the resultant force acting on the particle?

A person of height 1.6 m is walking away from a lamp post of height 4 m along a straight line on the horizontal ground. The lamp post and the person are always vertical. If the speed of the person is 60 cm/sec, then find the speed of tip point of its shadow with respect to the person in cm/sec.