A point particle of mass 0.1kg is excecuting SHM of amplitude 0.1m. When the particle passes through the mean position, its kinetic energy is `8xx10^(-3)` J. Obtain the equation of motion of the particle if the initial phase’of oscillation is `45^@`.

A particle of mass 10 g executing SHM has a velocity of 6cm s^(-1) after one second of its starting from the mean position. If the time period is 6 seconds, find its maximum kinetic energy.

A body is executing SHM. When its displacement from the mean position is 4 cm and 5 cm, the corresponding velocities of the particle are 10cm/s and 8 cm/s. The time period is

A body of mass 10 kg is rotating on a circular path of radius 1 m with time period 3.14S. Calculate its angular momentum and rotational kinetic energy.

A bob of mass 0.1 kg hung from the ceiling of a room by a string 2 m long is set into oscillation. The speed of the bob at its mean position is 1 m s^1. What is the trajectory of the bob if the string is cut when the bob is (a) at one of its extreme positions, (b) at its mean position.

The displacement equation of a particle moving along a straight line with uniform acceleration is x = v_0t + 1/2at^2 . Find the distance covered by the particle in the last second of its motion.

The position of particle is given by vecr=3.0thati-2.0t^2hatj+4.0hatk . Find the magnitude and direction of velocity of the particle at t=1.0s.

A solid cylinder of mass 20 kg rotates about its axis with angular speed 100 rad s-^1. The radius of the cylinder is 0.25 m. What is the kinetic energy associated with the rotation of the cylinder? What is the magnitude of angular momentum of the cylinder about its axis?

The blades of a windmill sweep out a circle of area A. (a) If the wind flows at a velocity v perpendicular to the circle, what is the mass of the air passing through it in time f?(b) What is the kinetic energy of the air? (c) Assume that the windmill converts 25% of the wind’s energy into electrical energy, and that A = 30 m^- 2 , v = 36 km/h and the density of air is 1.2 kg m^-3 . What is the electrical power produced?

A solid cylinder rolles down an inclined plane. Its mass is 2 kg and radius 0.1 m. If the height of the inclined plane is 4m, what is its rotational kinetic energy when it reaches the bottom.