Three particles P, Q and R are moving along the vectors $\overrightarrow{A}=\widehat{i}+\widehat{j},\overrightarrow{B}=\widehat{j}+\widehat{k}$  and $\overrightarrow{C}=-\widehat{i}+\widehat{j}$  respectively. They strike on point and start to move in different directions. Now particle P is moving normal to the plane which contains vector $\overrightarrow{A}and\overrightarrow{B}.$  Similarly particle Q is moving normal to the plane which contains vector $\overrightarrow{A}and\overrightarrow{C}.$  The angle between the direction of motion of P and Q $co{s}^{-1}\left(\frac{1}{\sqrt[]{x}}\right).$  Then the value of x 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