A galvanometer of resistance ' $G$ ' can be converted into a voltmeter of range ( $0-\mathrm{V}$ ) volt by connecting a resistance ' $R$ ' in series with it. The resistance ' $R$ required to change its range from $\left(0-\frac{\mathrm{V}}{4}\right)$ volt will be
A light metal disc of radius ' $r$ ' floats on water surface and bends the surface downwards along the perimeter making an angle ' $\theta$ ' with the vertical edge of the disc. If the weight of water displaced by the disc is ' W ', the weight of the metal disc is [ $\mathrm{T}=$ surface tension of water]
The magnetic field at the centre of a current carrying circular coil of area ' $A$ ' is ' $B$ '. The magnetic moment of the coil is ( $\mu_0=$. permeability of free space)
A parallel combination of two capacitors of capacities ' C ' and ' $\frac{\mathrm{C}}{3}$, respectively is connected across a battery of 12 volt. When both capacitors are fully charged, the charge and energy stored in them is $Q_1, Q_2$ and $E_1, E_2$ respectively. Then the ratio of $\left(E_1-E_2\right)$ to $\left(Q_1-Q_2\right)$ is