The density of a rod AB continuously increases from A to B. Is it easier to set it in rotatio by clamping ilt at A and applying a perpendicular force at B or by clamping it at B and applying the force at A?

AB is a line segment and line l is its perpendicular bisector. If a point P lies on l, show that P is equidistant from A and B.

A uniform rod of mass M and length a lies on a smooth horizontal plane. A particle of mass m moving at a speed v perpendicular to the length of the rod strikes it at a distance a/4 from the centre and stops after the collision. Find a. the velocity of the cente of the rod and b. the angular velocity of the rod abut its centre just after the collision.

A body of mass 'm' is kept on the horizontal floor and it is pushed in the horizontal direction with a force of 10N continuously, so that it moves steadily. (a) Draw FBD (a diagram showing all the forces acting on the body at a point of time) (b) What is the value of friction ?

Consider4 the situation shown in figure. Bothe the pulleys and the string are light and all the surfaces are friction less. a. Find the acceleration of the mass M. b. Find the tension in the string c. Calculate the force exerted by the clamp on the pulley A in the figure.

Shows a conducting circular loop of radius a placed in a uniform, perpendicular magnetic field B. A thick metal rod OA is pivoted at the Centre O. The other end of the rod touches the loop at A. The centre O and a fixed point C on the loop are connected by a wire OC of resistance R. A force is applied at the middle point of the rod OA perpendicularly, so that the rod rotates clockwise at a uniform angular velocity omega . Find the force.

A uniform rod of mass m and length l is struck at an end by a force F perpendicular to the rod for a short time interval t. Calculate a. the speed of the centre of mass ,b. the angular speed of the rod about centre of mass, c. the kinetic energy of the rod and d. the angular moment of the rod about the centre of mass after the force has stopped to act. Assume that t is so small that the rod does not apreciably change its direction while the force acts.

Consider a variation of the previous problem. Suppose the circular loop lies in a vertical plane. The rod has a mass m. The rod and the loop have negligible resistances but the wire connecting O and C has a resistance R. The rod is made to rotate with a uniform angular velocity omega in the clockwise direction by applying a force at the midpoint of OA in a dirction perpendicular ot it. find the magnitude of this force when the rod makes an angle theta with the vertical.

A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is at the mid-point of AB going towards A.

A particle is in linear simple harmonic motion between two points, A and B, 10 cm apart. Take the direction from A to B as the positive direction and give the signs of velocity, acceleration and force on the particle when it is at 3 cm away from A going towards B.