A high jumper successully clears the bar. Is it possibe that his centre of mass crossed the bar from below it? Try it with appropriate figures.

A man whose mass is m kg jumps vertically into air from a sitting position in which his centre of mass is at a height h_(1) from the ground. When his feet are just about to leave the ground his centre of mass is h_(2) from the ground and finally rises to h_(3) when he is at top of the jump . What is the average upwards force exerted by the ground on him ?

From a circular disc of radius R , a triangular portion is cut (see figure). The distance of the centre of mass of the remainder from the centre of the disc is -

A uniform thin cylindrical disk of mass M and radius R is attaached to two identical massless springs of spring constatn k which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is massless and both the springs and the axle are in horizontal plane. the unstretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity vecV_0 = vacV_0hati. The coefficinet of friction is mu. The centre of mass of the disk undergoes simple harmonic motion with angular frequency omega equal to -

A uniform thin cylindrical disk of mass M and radius R is attaached to two identical massless springs of spring constatn k which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is massless and both the springs and the axle are in horizontal plane. the unstretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity vecV_0 = vacV_0hati. The coefficinet of friction is mu. The maximum value of V_0 for whic the disk will roll without slipping is-

A uniform thin cylindrical disk of mass M and radius R is attaached to two identical massless springs of spring constatn k which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is massless and both the springs and the axle are in horizontal plane. the unstretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity vecV_0 = vacV_0hati. The coefficinet of friction is mu. The net external force acting on the disk when its centre of mass is at displacement x with respect to its equilibrium position is.

A non-uniform rod of mass m , length l and radius r is having its centre of mass at a distance l//4 from the centre and lying on the axis of the cylinder. The cylinder is kept in a liquid of uniform density rho . The moment of inertia of the rod about the centre of mass is I . The angular acceleration of point A relative to point B just after the rod is released from the position as shown in the figure is

A short bar magnet of magnetic moment 5.25 xx 10^(-2) JT^(-1) is placed with its axis perpendicular to the earth's field direction. At what distance from the centre of the magnet, the resultant field is inclined at 45^@ with earth's field on (a) its normal bisector and (b) its axis. Magnitude of the earth's fleld at the place is given to be 0.42 G. Ignore the length of the magnet in comparison to the distances involved.

The ends of a long bar are maintained at different temperatures and there is no loss of heat from the sides of the bar due to conduction or radiation. The graph of temperature against distance of the bar when it has attained steady state is shown here. The graph shows ltimg src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/ALN_PHY_R03_E09_009_Q01.png" width="80%"gt (i) the temperature gradient is not uniform. (ii) the bar has uniform cross-sectional area. (iii) the cross-sectional area of the bar increases as the distance from the hot end increases. (iv) the cross-sectional area of the bar decreases as the distance from the hot end increases

A mass M is in static equilibrium on a massless vertical spring as shown in the figure. A ball of mass m dropped from certain height sticks to the mass M after colliding with it.The oscillations they perform reach to height a above the original level of scales & depth 'b' below it. (a) Find the constant of force of the spring., (b) Find the oscillation frequency.