Laws of Motion ...

A block is placed on an inclined plane. The angle of inclination () of the plane is such that the block slides down the plane at a constant speed. The coefficient of kinetic friction between the block and the inclined plane is equal to

When several forces act on a body

In the arrangement shown in the figure below, the strings are light and inextensible. The surface over which the blocks are placed is smooth. What is the acceleration of each block?

Second law in terms of momentum p and mass m is

A block of mass 2 kg is placed on the surface of a trolley of mass 20 kg, which is on a smooth surface. The coefficient of friction between the block and the surface of the trolley is 0.25. If a horizontal force of 2 N acts on the block, then the acceleration of the system (in ms^-2) (g = 10 ms^-2) is

Force is a

A disc of radius r = 20 cm is rotating about its axis with an angular speed of 20 rad s^–1_. It is gently placed on a horizontal surface which is perfectly frictionless (as shown in the figure). What is the linear speed of point A on the disc?

The following figure is part of a horizontally stretched net. Section 'AB' is stretched with a force of 10 N. The tensions in the sections 'BC' and 'BF', respectively, are

A frictionless track ABCDE ends in a circular loop of radius R. A body slides down the track from point A which is at a height h = 5 cm. What is the maximum value of R for the body to successfully complete the loop?

An ice cart of mass 60 kg rests on a horizontal snow patch with coefficient of static friction 1/3. Assuming that there is no vertical acceleration, find the magnitude of the minimum horizontal force required to move the ice cart. (g = 9.8ms^-2)

A car is moving in a circular track of radius 10 m with a constant speed of 10 m/s. A plumb bob is suspended from the roof of the car by a light rigid rod of length 1 m. The angle made by the rod with the vertical is   ( take g = 10 m/s²)

Directions: The following question has four choices out of which ONLY ONE is correct.

A particle moves in a circle of radius 25 cm at the rate of two revolutions per second. The acceleration of particle is

A rock weighing 30 N falls from a height of 15 m and sinks 0.5 m into the ground. The average force between the rock and the ground, as the rock sinks, is

Two masses M and M/2 are joined together by means of a light inextensible string and passed over a frictionless pulley as shown in the figure. When the bigger mass is released, the smaller one will ascend with an acceleration of

A body is dropped from height h. If the coefficient of restitution is e, then calculate the height achieved after one bounce.

A car of mass 800 kg moves on a circular track of radius 40 m. If the coefficient of friction is 0.5, then the maximum velocity with which the car can move is

What should be the angle of banking for speed v and curved track of radius r?

A body takes time t to reach the bottom of an inclined plane of angle θ with the horizontal. If the plane is made rough, time taken now is 2t. The coefficient of friction of the rough surface is

second law of motion  in terms of acceleration a⃗  and mass m of a body is

The v-t graph of a linear motion is shown in adjoining figure. What is the distance from origin after 8 seconds?

If a body is in equilibrium

The pulleys and the strings shown in the figure are smooth and of negligible mass. For the system to remain in equilibrium, angle θ should be

The combined mass of a rider and a motorcycle is 200 kg. The rider is to negotiate a curve of 80 m radius at a speed of 72 kmh^–1. The angle at which the rider must lean to avoid falling is given by (Take g = 10 ms^–2)

A stone of mass 200 g is tied to the end of a 1 m long string. Holding the string at the other end, it is whirled in horizontal circles. If the speed of the stone is 10 m/s, calculate the centripetal force.

An elevator car whose floor to ceiling distance is equal to 2.7 m starts ascending with constant acceleration of 1.2 m/s². 2 sec after the start, a bolt begins falling from the ceiling of the car. What is the free fall time of the bolt? (g = 9.8 m/s²)