Equation of travelling wave on a stretched string of linear density \(5\,g/m\) is \(y = 0.03\,sin\,(450\,t -9x)\) where distance and time are measured in \(SI\) united. The tension in the string is ... \(N\)

A ray of light is incident from air on a glass plate having thickness \(\sqrt{3} \,cm\) and refractive index \(\sqrt{2}\). The angle of incidence of a ray is equal to the critical angle for glass-air interface. The lateral displacement of the ray when it passes through the plate is \(.......\times 10^{-2}\) (given \(\sin 15^{\circ}=0.26\) )

\({ }_{92}^{238} A \rightarrow{ }_{90}^{234} B +{ }_2^4 D + Q\) In the given nuclear reaction, the approximate amount of energy released will be \(.....\,MeV\) \(\text { [Given, mass of }{ }_{92}^{238} A =238.05079 \times 931.5\,MeV / c ^2\) \(\text { mass of }{ }_{90}^{234} B =234.04363 \times 931.5\,MeV / c ^2\) \(\text { mass of } \left.{ }_2^4 D =4.00260 \times 931.5\,MeV / c ^2\right]\)

Seven identical circular planar disks, each of mass \(M\) and radius \(R\) are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point \(P\) is:

A sample of gas with \(\gamma=1.5\) is taken through an adiabatic process in which the volume is compressed from \(1200\, {cm}^{3}\) to \(300\, {cm}^{3}\). If the initial pressure is \(200\, {kPa}\). The absolute value of the workdone by the gas in the process \(= \,..... J.\)

Given below are two statements: Statement \(I :\) In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution. Statement \(II :\) In a diatomic molecule, the rotational energy at a given temperature equals the translational kinetic energy for each molecule. In the light of the above statements, choose the correct answer from the options given below:

An astronaut takes a ball of mass \(m\) from earth to space. He throws the ball into a circular orbit about earth at an altitude of \(318.5 \mathrm{~km}\). From earth's surface to the orbit, the change in total mechanical energy of the ball is \(x \frac{\mathrm{GM}_e \mathrm{~m}}{21 R_e}\). The value of \(x\) is _______. (take \(R_{\mathrm{e}}=6370 \mathrm{~km}\) )

The volume of an ideal gas increases 8 times and temperature becomes (1/4) of initial temperature during a reversible change. If there is no exchange of heat in this process (\( \Delta Q=0 \)) then identify the gas from the following options: