A particle is moving along the $x$ $$ -axis with its coordinate with time ' $t$ $$ ' given by $x\left(t\right)=10+8t-3t^2$ ${}^{}$ . Another particle is moving along the $$ $y$ -axis with its coordinate a function of time given by $y\left(t\right)=5-8t^3$ ${}^{}$ . At $t=1\mathrm{s}$ $$ , the speed of the second particle as measured in the frame of the first particle is given as $\sqrt[]{v}$ $\text{exception 25:}$ . Then $v$ $$ (in $$ ) $\mathrm{m}/\mathrm{s}$ is

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