If a charge \(q\) is placed at the centre of a closed hemispherical non-conducting surface, the total flux passing through the flat surface would be

From a sphere of mass \(M\) and radius \(R\), a smaller sphere of radius \(\frac{R}{2}\) is carved out such that the cavity made in the original sphere is between its centre and the periphery (See figure) . For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is \(3R\), the gravitational force between the two sphere is

There are \(100\) divisions on the circular scale of a screw gauge of pitch \(1 \mathrm{~mm}\). With no measuring quantity in between the jaws, the zero of the circular scale lies \(5\) divisions below the reference line. The diameter of a wire is then measured using this screw gauge. It is found the \(4\) linear scale divisions are clearly visible while \(60\) divisions on circular scale coincide with the reference line. The diameter of the wire is _______.

Given below are two statements : Statement \(I :\) Stopping potential in photoelectric effect does not depend on the power of the light source. Statement \(II :\) For a given metal, the maximum kinetic energy of the photoelectron depends on the wavelength of the incident light. In the light of above statements, choose the most appropriate answer from the options given below. Options :

Two satellites \(S _{1}\) and \(S _{2}\) are revolving in circular orbits around a planet with radius \(R _{1}=3200 \,km\) and \(R _{2}=800\, km\) respectively. The ratio of speed of satellite \(S_{1}\) to the speed of satellite \(S_{2}\) in their respective orbits would be \(\frac{1}{ x }\) where \(x =\)

A square loop of edge length \(2 \mathrm{~m}\) carrying current of \(2 \mathrm{~A}\) is placed with its edges parallel to the \(\mathrm{x}-\mathrm{y}\) axis. A magnetic field is passing through the \(x-y\) plane and expressed as \(\vec{B}=B_0(1+4 x) \hat{k}\), where \(\mathrm{B}_0=5 \mathrm{~T}\). The net magnetic force experienced by the loop is _______ \(\mathrm{N}\).

\(5\,g\) and radius \(1\,cm\) is fixed to a thin stick \(AB\) of negligible mass as shown in the figure. The system is initially at rest. The constant torque, that will make the system rotate about \(AB\) at \(25\) rotations per second in \(5\,s\) is close to

A potential \(V_0\) is applied across a uniform wire of resistance \(R\). The power dissipation is \(P_1\). The wire is then cut into two equal halves and a potential of \(V _0\) is applied across the length of each half. The total power dissipation across two wires is \(P_2\). The ratio \(P_2: P_1\) is \(\sqrt{x}: 1\). The value of \(x\) is \(.............\).

In a metre-bridge when a resistance in the left gap is \(2\ \Omega\) and unknown resistance in the right gap, the balance length is found to be \(40\ \mathrm{cm}\). On shunting the unknown resistance with \(2\ \Omega\), the balance length changes by _______.

Which of the following pair of nuclei are isobars of the element?

In an electromagnetic wave the electric field vector and magnetic field vector are given as \(\vec{E}=E_{0} \hat{i}\) and \(\vec{B}=B_{0} \hat{k}\) respectively. The direction of propagation of electromagnetic wave is along.