A partiale of mass m is moving in a circular path of radius r such that its centripetal acceleration is varying with time t as `a_c = k^2rt^2, where k is constant. The power delivered to the particle by the forces acting on it is

If two bodies have circular path of radius rt and r2 and the time taken are the same, find the ratio of the -angular speed.

Magnitude of force F experienced by a certain object moving with speed v is given by F = Kv^2 where K is a constant. Find the dimensions of K.

A particle moves along a straight line according to x = Pt^2 + 2qt + r where x is the distance travelled in time t and p, q and r are constants. Find an expression for the acceleration of the particle.

The distance x of a particle moving in one dimension, under the action of constant force is related to time t by equation. t = sqrt x + 3 where x in metre and t in second. Find the displacement of the particle when its velicity is zero.

Define the co-efficient of restitution. A particle of a mass m moving with a velocity u struck head-on against another particle of mass Km at rest.After collision the particles move with velocities V1 and V2 respectively.If the collision is prefectly elastic.Prove that the loss of kinetic energyof the particle with mass m is maximum when k=1.

A body is initially at rest. It Undergoes one-dimensional motion with constant acceleration. The power delivered to it at time t is proportional to(i)t(1)/2 (ii)t(iii)t(2)/3(iv) t^2

MI of a thin circular disc about an axis passing through its centre and perpendicular to its plane is 1/2 MR^2 , where M is the mass of the disc and R is its radius. Find an expression for radius of gyratiuon of the disc about an axis tangential to the edge and peerpendicular to the plane of rotation.

One end of a string of length l is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v the net force on the particle (directed towards the centre) is: (i)T,(II) T-(mv^2)//l, (iii) T+(MV^2)/l, (iv)0

A partical of mass m1 is travelling with avelocity u1 strikes head-on against partical of mass m2 at rest.After collision the particales move with a velocity v1 and v2 respectively .show that the ratio of decrese in K.E of the partical of mass m1 to its original K.E is given By (4m1m2)/(m1+m2)^2

(a) Find the moment of inertia of a sphere about a tangent to the sphere, given the moment of inertia of the sphere about any of its diameters to be 2MR^2IS, where M is the mass of the sphere and R is the radius of the sphere(b) Given the moment of inertia of a disc of mass M and radius R about any of its diameters to be MR2I4, find its moment of inertia about an axis normal to the' disc and passing through a point on its edge.