If the charge on a capacitor is increased by \(2C\), the energy stored in it increases by \(44 \%\). The original charge on the capacitor is (in \(C\) )

Two identical charged spheres are suspended by string of equal lengths. The string make an angle of \(37^{\circ}\) with each other. When suspended in a liquid of density \(0.7 \mathrm{~g} / \mathrm{cm}^3\), the angle remains same. If density of material of the sphere is \(1.4 \mathrm{~g} / \mathrm{cm}^3\), the dielectric constant of the liquid is _______\(\left(\tan 37^{\circ}=\frac{3}{4}\right)\).

As shown in the figure, a current of \(2\,A\) flowing in an equilateral triangle of side \(4 \sqrt{3}\,cm\). The magnetic field at the centroid \(O\) of the triangle is: (Neglect the effect of earth's magnetic field.)

An object is at a distance of \(20\,m\) from a convex lens of focal length \(0.3\,m.\) The lens forms an image of the object. If the object moves away from the lens at a speed of \(5\,m/s,\) the speed and direction of the image will be

In order to determine the Young's Modulus of a wire of radius \(0.2\, cm\) (measured using a scale of least count \(=0.001\, cm )\) and length \(1 \,m\) (measured using a scale of least count \(=1\, mm\) ), a weight of mass \(1\, kg\) (measured using a scale of least count \(=1 \,g\) ) was hanged to get the elongation of \(0.5\, cm\) (measured using a scale of least count \(0.001\, cm\) ). What will be the fractional error in the value of Young's Modulus determined by this experiment? (in \(\%\))

To project a body of mass \(m\) from earth's surface to infinity, the required kinetic energy is _______. (assume, the radius of earth is \(R_E, g=\) acceleration due to gravity on the surface of earth)

The total charge enclosed in an incremental volume of \(2 \times 10^{-9} \,{m}^{3}\) located at the origin is ...... \(nC,\) if electric flux density of its field is found as \(D=e^{-x} \sin y \hat{i}-e^{-x} \cos y \hat{j}+2 z \hat{k}\, C / m^{2}\)

Choose the correct statement for processes \(A\)  & \(B\) shown in figure.

The ratio of wavelengths of proton and deuteron accelerated by potential \(V_{p}\) and \(V_{d}\) is 1: \(\sqrt{2}\). Then, the ratio of \(V_{p}\) to \(V_{d}\) will be

Curved surfaces of a plano-convex lens of refractive index \(\mu_{1}\) and a plano-concave lens of refractive index \(\mu_{2}\) have equal radius of curvature as shown in figure. Find the ratio of radius of curvature to the focal length of the combined lenses.