System of Particles and Rotational Motion

A particle of mass m is projected with a velocity 'u' making an angle of 30 with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height h is :

1. mu3 2 g
2. zero
3. 32 mu2g
4. 316 mu3g

[figure] Consider a Disc of mass 5 kg, radius 2 m, rotating with angular velocity of 10 rad/s about an axis perpendicular to the plane of rotation. An identical disc is kept gently over the rotating disc along the same axis. The energy dissipated so that both the discs continue to rotate together without slipping is J.

Two discs of moment of inertia I1=4 kg m2 and I2=2 kg m2, about their central axes & normal to their planes, rotating with angular speeds 10 rad/s & 4 rad/s respectively are brought into contact face to face with their axes of rotation coincident. The loss in kinetic energy of the system in the process is J.

A cylinder is rolling down on an inclined plane of inclination 60 . Its acceleration during rolling down will be x 3 m/s2, where x= (use g=10 m/s2).

A body of mass 5 kg moving with a uniform speed 3 2 ms-1 in X-Y plane along the line y=x+4. The angular momentum of the particle about the origin will be kg m2 s-1.

Four particles each of mass 1 kg are placed at four corners of a square of side 2 m. Moment of inertia of system about an axis perpendicular to its plane and passing through one of its vertex is kg m2. [figure]

A heavy iron bar of weight 12 kg is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle 60 with the horizontal, the weight experienced by the man is :

1. 3 kg
2. 6 kg
3. 6 3 kg
4. 12 kg

A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of their kinetic energies is 7x, where x is .