In the circuit shown, charge on the \(5\, \mu F\) capacitor is\(........\mu C\)

The gravitational field in a region is given by \(\overrightarrow g  = 5\,N/kg\hat i\, + \,12\,N/kg\hat j\). The change in the gravitational potential energy of a particle of mass \(1\, kg\) when it is taken from the origin to a point \((7\, m, - 3\, m)\) is .......  \(J\)

If the magnetic field of a plane electromagnetic wave is given by (The speed of light \( = 3 \times {10^8}\,m/s\) ) \(B = 100 \times {10^{ - 6}}\,\sin \,\left[ {2\pi  \times 2 \times {{10}^{15}}\,\left( {t - \frac{x}{c}} \right)} \right]\)  then the maximum electric field associated with it is

Consider a solid sphere of radius \(\mathrm{R}\) and mass density \(\rho(\mathrm{r})=\rho_{0}\left(1-\frac{\mathrm{r}^{2}}{\mathrm{R}^{2}}\right),  0<\mathrm{r} \leq \mathrm{R} .\) The minimum density of a liquid in which it will float is

The refractive index of prism is \(\mu=\sqrt{3}\) and the ratio of the angle of minimum deviation to the angle of prism is one. The value of angle of prism is _______ \(^\circ\).

A particle of mass \({m}\) is suspended from a ceiling through a string of length \(L\). The particle moves in a horizontal circle of radius \(r\) such that \({r}=\frac{{L}}{\sqrt{2}}\). The speed of particle will be:

In a meter bridge experiment, the circuit diagram and the corresponding observation table are shown in figure

\(Sl\). \(No\).	\(R\, (\Omega )\)	\(l\, (cm)\)
\(1\).	\(1000\)	\(60\)
\(2\).	\(100\)	\(13\)
\(3\).	\(10\)	\(1.5\)
\(4\).	\(1\)	\(1.0\)

Which of the readings is inconsistent ?

A charged particle (mass \(m\) and charge \(q\) ) moves along \(X\) axis with velocity \(V _{0}\). When it passes through the origin it enters a region having uniform electric field \(\overrightarrow{ E }=- E \hat{ j }\) which extends upto \(x = d\). Equation of path of electron in the region \(x > d\) is 

A thin ring of \(10\, cm\) radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of \(40\,\pi \,rad\,{s^{ - 1}}\) about its axis, perpendicular to its plane. If the magnetic field at its centre is \(3.8 \times {10^{ - 9}}\,T\), then the charge carried by the ring is close to \(\left( {{\mu _0} = 4\pi  \times {{10}^{ - 7}}\,N/{A^2}} \right)\)