If \(\mathrm{G}\) be the gravitational constant and \(\mathrm{u}\) be the energy density then which of the following quantity have the dimension as that the \(\sqrt{\mathrm{uG}}\)?

A boy is rolling a \(0.5\, kg\) ball on the frictionless floor with the speed of \(20\, ms ^{-1}\). The ball gets deflected by an obstacle on the way. After deflection it moves with \(5 \%\) of its initial kinetic energy. What is the speed of the ball now ? (in \(ms ^{-1}\))

In an experiment of \(CE\) configuration of \(n-p-n\) transistor, the transfer characteristics are observed as given in figure. If the input resistance is \(200 \Omega\) and output resistance is \(60 \Omega\) the voltage gain in this experiment will be..........

An infinitely long straight wire carrying current \(I,\) one side opened rectangular loop and a conductor \(C\) with a sliding connector are located in the same plane, as shown in the figure. The connector has length \(l\) and resistance \(R\). It slides to the right with a velocity \(V.\) The resistance of the conductor and the self inductance of the loop are negligible. The induced current in the loop, as a function of separation \(r,\) between the connector and the straight wire is

A planet having mass \(9\,Me\) and radius \(4 R _e\), where Me and \(\operatorname{Re}\) are mass and radius of earth respectively, has escape velocity in \(km / s\) given by:(Given escape velocity on earth \(\left.V_e=11.2 \times 10^3\,m / s \right)\)

A thin circular disc is in the \(xy\) plane as shown in the figure. The ratio of its moment of inertia about \(z\)  and \(z'\)  axes will be

If speed \(V,\) area \(A\) and force \(F\) are chosen as fundamental units, then the dimension of Young's modulus will be :

A sample of an ideal gas is taken through the cyclic process \(abca\) as shown in the figure. The change in the internal energy of the gas along the path \(ca\) is \(-180\, J\). The gas absorbs \(250\, J\) of heat along the path \(ab\) and \(60\, J\) along the path \(bc\). The work done by the gas along the path \(abc\) is ..... \(J\)

The current flowing through \(R _2\) is:

A bicycle tyre is filled with air having pressure of \(270\,kPa\) at \(27^{\circ}\,C\). The approximate pressure of the air in the tyre when the temperature increases to \(36^{\circ}\,C\) is \(............kPa\)

An object ' \(o\) ' is placed at a distance of \(100\,cm\) in front of a concave mirror of radius of curvature \(200\,cm\) as shown in the figure. The object starts moving towards the mirror at a speed \(2\,cm / s\). The position of the image from the mirror after \(10\,s\) will be at ...... \(cm\).

The current in an inductor is given by \(\mathrm{I}=(3 \mathrm{t}+8)\) where \(t\) is in second. The magnitude of induced emf produced in the inductor is \(12 \mathrm{mV}\). The selfinductance of the inductor _______ \(\mathrm{mH}\).