Physics System of Particles and Rotational Motion

A mass M hangs on a massless rod of length l which rotates at a constant angular frequency. The mass M moves with steady speed in a circular path of constant radius. Assume that the system is in steady circular motion with constant angular velocity ω. The angular momentum of M about point A is LA which lies in the positive z direction and the angular momentum of M about point B is LB. The correct statement for this system is:

A triangular plate is shown. A force F = 4i - 3j is applied at point P. The torque at point P with respect to point 'O' and 'Q' are :

The centre of mass of a solid hemisphere of radius 8 cm is x cm from the centre of the flat surface. Then value of x is

The linear mass density of a thin rod AB of length L varies from A to B as λ(x) = λ₀ (1 + x/L), where x is the distance from A. If M is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular to the rod is:

For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through O (the centre of mass) and O' (corner point) is:

A circular coil has moment of inertia 0.8 kg m² around any diameter and is carrying current to produce a magnetic moment of 20Am². The coil is kept initially in a vertical position and it can rotate freely around a horizontal diameter. When a uniform magnetic field of 4 T is applied along the vertical, it starts rotating around its horizontal diameter. The angular speed the coil acquires after rotating by 60° will be:

Consider two uniform discs of the same thickness and different radii R₁ = R and R₂ = aR made of the same material. If the ratio of their moments of inertia I₁ and I₂, respectively, about their axes is I₁:I₂ = 1:16 then the value of a is:

A circular disc of mass M and radius R is rotating about its axis with angular speed ω₁. If another stationary disc having radius R/2 and same mass M is dropped co-axially on to the rotating disc. Gradually both discs attain constant angular speed ω₂. The energy lost in the process is p% of the initial energy. Value of p is
(Rotational)

ABC is a plane lamina of the shape of an equilateral triangle. D, E are mid points of AB, AC and G is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through G and perpendicular to the plane ABC is I?. If part ADE is removed, the moment of inertia of the remaining part about the same axis is NI?/16 where N is an integer. Value of N is