Physics Test - ...

A particle moving along \(x\) -axis has acceleration \('f'\) at time \('t'\), given by where \(f 0^{\prime}\) and \(T^{\prime}\) are constants. The particle at ' \(t^{\prime}=0\) has zero velocity. In the time interval between ' \(t^{\prime}=0\) and the instant when \(f^{\prime}=0\), the velocity \((vx)\) of the particle is

\(1 kg\) of water at \(100^{\circ} C\) is converted into steam at \(100^{\circ} C\) by boiling at atmospheric pressure. The volume of water changes from \(1.00 \times 10^{-3} m ^3\) as a liquid to 1. \(671 m ^3\) as steam. The change in internal energy of the system during the process will be (Given latent heat of vaporisation \(=2257 kJ / kg\), Atmospheric pressure \(\left.=1 \times 10^5 Pa \right)\)

The magnetic field vector of an electromagnetic wave is given by \(B=B_0 \frac{\hat{i}+\hat{j}}{\sqrt{2}} \cos (k z-\omega t) T\) where \(\hat{i}, \hat{j}\) represents unit vector along \(X\) and \(Y\)-axis respectively. At \(t=0\), two electric charges \(q_1\) of \(4 \pi \mathrm{C}\) and \(\mathrm{q}_2\) of \(2 \pi \mathrm{C}\) located at \(\left(0,0, \frac{\pi}{\mathrm{k}}\right)\) and \(\left(0,0, \frac{3 \pi}{\mathrm{k}}\right)\) respectively, have the same velocity of \(0.5 \mathrm{c} \hat{i}\). (where, \(c\) is the velocity of light). The ratio of the force acting on charge \(q_1\) to \(q_2\) is

A solenoid of inductance \(L\) and resistance \(R\) is connected to a battery. The time taken for the magnetic energy to reach \(\frac{1}{4}\) of its maximum value is:

A star initially has \(10^{40}\) deuterons. It produces energy through the processes

\({ }_{1} H ^{2}+{ }_{11} H ^{2} \rightarrow{ }_{2} H ^{3}+ P\) and \({ }_{1} H ^{2}+{ }_{1} \rightarrow{ }_{2} H e ^{4}+ n\)

If the average power radiated by the star is \(10^{16} W\), the deuteron supply of the star is exhausted in a time of the order of

A tank is filled with water of density \(1 \frac{{~g}}{{cm}^{3}}\) and oil of density \(0.9 \frac{{~g}}{{cm}^{3}}\). The height of water layer is \(100 {~cm}\) and that of oil layer is 400 \({cm}\). If \(g=980 \frac{{~cm}}{{s}^{2}}\), then the velocity of efflux from an opening in the bottom of the tank will be-

A clock that keeps correct time at \(25^{\circ} C\) has a pendulum made of metal. The temperature falls to \(0^{\circ} C .\) If the coefficient of linear expansion of the metal is \(1.9 \times 10^{-5}\) per \(^{\circ} C\), then find the number of seconds the clock gains per day.

If a body is rolling down from a hill at certain height, the body will have:

\(ABCDA\) is a cyclic process explaining the thermodynamic process. What is the work done by the system in the cycle?

A short bar magnet placed with its axis at \(30^{\circ}\) with a uniform external magnetic field of \(0.25 \mathrm{~T}\) experiences a torque of magnitude equal to \(4.5 \times 10^{-2} \mathrm{~J}\). What is the magnitude of magnetic moment of the magnet?