A particle $(m=1\mathrm{k}\mathrm{g})$  slides down a frictionless track (AOC) starting from rest of a point $A$  (height $2\mathrm{m}$  ). After reaching $C$ , the particle continues to move freely in air as a projectile. When it leading its highest point $\mathrm{P}$  (height 1 m  ) the kinetic energy of the particle (in J) is: (Figure drawn is schematic and not to scale (take $g=10{\mathrm{m}\mathrm{s}}^{-2}$  ) 

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