Mathematics Tes...

Let 'M' be the mass and 'L' be the length of a thin uniform rod. In first case, axis of rotation is passing through centre and perpendicular to the length of the rod. In second case axis of rotation is passing through one end and perpendicular to the length of the rod. The ratio of radius of gyration in first case to second case is :

Four small objects each of mass m are fixed at the corners of a rectangular wire-frame of negligible mass and of sides a and b (a>b). If the wire frame is now rotated about an axis passing along the side of length b, then the moment of inertia of the system for this axis of rotation is:

A metal bar of 70 cm long and 4 kg in mass supported on two knife edges placed 20 cm from each end. A 6 kg load is suspended at 30 cm from on end. Find the normal reaction at the knife-edge. (assume it to be of uniform cross section and homogeneous).

A round uniform body of radius R, mass M and moment of inertia I, rolls down (without slipping) an inclined plane making an angle with the horizontal. Then its acceleration is :

A uniform cube of side 'b' and mass M rest on a rough horizontal table. A horizontal force F is applied normal to one of the face at a point, at a height 3b/4 above the base. What should be the coefficient of friction (μ) between cube and table so that it will tip about an edge before it starts slipping?

Two persons P and Q of the same height are carrying a uniform beam of length 3m. If Q is at one end, then the distance of P from the other end such that P, Q receive loads in the ratio 5:3 is:

A solid cylinder is projected on a rough surface having coefficient of friction μ, with velocity v₀ and angular velocity ω₀=v₀/2r, (whre r is radius). What is the time t at which rolling without slipping occurs is :

If the Earth shrinks such that its density becomes 8 times its present value then the new duration of the day in hours will be : (assume that there is no change in axis of rotation of the earth)

Keeping the mass of earth as constant, if its radius is reduced to 1/4th of its initial value, then the period of revolution of earth about its own axis, and passing through the centre, in hrs, is:

(Assume earth to be a solid sphere and its initial period of rotation as 24 hrs)

A spaceship is launched into a circular orbit of radius R close to the surface of earth. The additional velocity to be imparted to the spaceship in the orbit to overcome the earth's gravitational pull is : ( g= acceleration due to gravity )