A balloon is moving up in air vertically above a point A on the ground. When it is at a height h₁, a girl standing at a distance d (point B) from A (see figure) sees it at the angle 45° with respect to the vertical. When the balloon climbs up a future height h₂, it is seen at the angle 60° with respect to the vertical if the girl moves further by a distance 2.464 d (point C). Then the height h₂ is (given tan 30° = 0.5774) :

 

Two SHMs in same direction are represented by y1 = asinωt and y2 = asin(ωt + δ). When they superimpose, the initial phase difference of the resultant SHM is

The potential energy of a particle of mass 2 kg in motion along the x-axis is given by U = 2 (1 – cos 2x) J, where x is in meters. The period of small oscillations (in s) is

A child is standing with folded hands at the centre of a platform rotating about its central axis. The kinetic energy of the system is K. The child now stretches his arms so that the moment of inertia of the system becomes 3/2 of the initial moment of inertia. The kinetic energy of the system is now

If the absolute temperature of hot black body is raised by 2%, by how much percentage rate of heat energy radiated would be increased nearly?

Two moles of helium gas are taken over the cycle ABCDA as shown below in P-T diagram. Assuming the gas to be ideal, the work done on the gas in taking from A to B is