An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being $68\mathrm{k}\mathrm{g}$ . The mass of the elevator itself is $920\mathrm{k}\mathrm{g}$ and it moves with a constant speed of $3\mathrm{m}/\mathrm{s}$ . the frictional force opposing the motion is $6000\mathrm{N}$ . If the elevator is moving up with its full capacity, the power delivered by the motor to the elevator $\left(\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2\right)$  must be at least:

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