In the reported figure, two bodies \(A\) and \(B\) of masses \(200\, {g}\) and \(800\, {g}\) are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be \(.....\,{rad} / {s}\) when \({k}=20 \,{N} / {m} .\)

A Carnot engine take \(5000 \,k\,cal\) of heat from a reservoir at \(727\,^{\circ}C\) and gives heat to a \(\operatorname{sink}\) at \(127\,^{\circ}C\). The work done by the engine is \(.......... \times 10^{6}\,J\)

The acceleration due to gravity is found upto an accuracy of \(4 \,\%\) on a planet. The energy supplied to a simple pendulum to known mass ' \({m}\) ' to undertake oscillations of time period \(T\) is being estimated. If time period is measured to an accuracy of \(3\, \%\), the accuracy to which \({E}\) is known as \(..........\,\%\)

In the given figure, the energy levels of hydrogen atom have been shown along with some transitions marked \(A. B, C. D\) and \(E.\) The transitions \(A , B\) and \(C\) respectively represent

An electron projected perpendicular to a uniform magnetic field B moves in a circle. If Bohr's quantization is applicable, then the radius of the electronic orbit in the first excited state is :

In a parallel plate capacitor set up, the plate area of capacitor is \(2 \,m ^{2}\) and the plates are separated by \(1\, m\). If the space between the plates are filled with a dielectric material of thickness \(0.5\, m\) and area \(2\, m ^{2}\) (see \(fig.\)) the capacitance of the set-up will be \(.........\, \varepsilon_{0}\) (Dielectric constant of the material \(=3.2\) ) and (Round off to the Nearest Integer)

A transistor is used in common-emitter mode in an amplifier circuit. When a signal of \(10\, mV\) is added to the base-emitter voltage, the base current changes by \(10 \mu A\) and the collector current changes by \(1.5 \,mA\). The load resistance is \(5 \,k \Omega\). The voltage gain of the transistor will be

The moment of inertia of semicircular ring about an axis, passing through the center and perpendicular to the plane of ring, is \(\frac{1}{ x } MR ^2\), where \(R\) is the radius and \(M\) is the mass of semicircular ring. The value of \(x\) will be \(...........\)

The frequency of echo will be \(.......Hz\) if the train blowing a whistle of frequency \(320\,Hz\) is moving with a velocity of \(36\,km / h\) towards a hill from which an echo is heard by the train driver. Velocity of sound in air is \(330\,m / s\).

An ideal monoatomic gas is confined in a cylinder by a spring loaded piston of cross section \(8.0\times10^{-3}\, m^2\) . Initially the gas is at \(300\, K\) and occupies a volume of \(2.4\times10^{-3}\, m^3\) and the spring is in its relaxed state as shown in figure. The gas is heated by a small heater until the piston moves out slowly by \(0.1\, m\). The force constant of the spring is \(8000\, N/m\) and the atmospheric pressure is \(1.0\times10^5\, N/m^2\) . The cylinder and the piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and the cylinder. The final temperature of the gas will be: (Neglect the heat loss through the lead wires of the heater . The heat capacity of the heater coil is also negligible)

The speed of sound in oxygen at \(S.T.P. \)will be approximately _______. (Given, \(\mathrm{R}=8.3 \mathrm{JK}^{-1}, \gamma=1.4\) )

Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by \(y=\left(10 \cos \pi x \sin \frac{2 \pi t}{T}\right)\, cm\) The amplitude of the particle at \(x =\frac{4}{3} \,cm\) will be........ \(cm\).

In the given figure, a body of mass \(M\) is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant \(k,\) the frequency of oscillation of given body is :