Identify the pair of physical quantities that have same dimensions

In the figure, a very large plane sheet of positive charge is shown. \(P _{1}\) and \(P _{2}\) are two points at distance \(l\) and \(2 \,l\) from the charge distribution. If \(\sigma\) is the surface charge density, then the magnitude of electric fields \(E_{1}\) and \(E_{2}\) at \(P _{1}\) and \(P _{2}\) respectively are

The space inside a straight current carrying solenoid is filled with a magnetic material having magnetic susceptibility equal to \(1.2 \times 10^{-5}\). What is fractional increase in the magnetic field inside solenoid with respect to air as medium inside the solenoid?

A moving coil galvanometer of resistance \(100 \Omega\) shows a full scale deflection for a current of 1 mA . The value of resistance required to convert this galvanometer into an ammeter, showing full scale deflection for a current of 5 mA , is _________ \(\Omega\)

In Young's double slit experiment, monochromatic light of wavelength \(5000\) \(A\) is used. The slits are \(1.0 \mathrm{~mm}\) apart and screen is placed at \(1.0 \mathrm{~m}\) away from slits. The distance from the centre of the screen where intensity becomes half of the maximum intensity for the first time is _______ \(10^{-6} \mathrm{~m}\).

A disc with a flat small bottom beaker placed on it at a distance \(R\) from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity \(\omega\). The coefficient of static friction between the bottom of the beaker and the surface of the disc is \(\mu\). The beaker will revolve with the disc if 

In a hydrogen like ion, the energy difference between the \(2^{\text {nd }}\) excitation energy state and ground is 108.8 eV. The atomic number of the ion is

The two thin coaxial rings, each of radius \('a'\) and having charges \(+{Q}\) and \(-{Q}\) respectively are separated by a distance of \('s'.\) The potential difference between the centres of the two rings is :

A cubical block of side \(30\,cm\)  is moving with  velocity \(2\,\,ms^{-1}\) on a smooth horizontal surface. The surface has a bump at a point \(O\) as shown in figure. The angular velocity (in rad/s) of the block immediately after it hits the bump, is

Consider two identical springs each of spring constant \(k\) and negligible mass compared to the mass \(M\) as shown. Fig. \(1\) shows one of them and Fig. \(2\) shows their series combination. The ratios of time period of oscillation of the two \(SHM\) is \(\frac{ T _{ b }}{ T _{ a }}=\sqrt{ x },\) where value of \(x\) is (Round off to the Nearest Integer)

In an electrical circuit drawn below the amount of charge stored in the capacitor is _______ \(\mu \mathrm{C}\).

A uniform sphere of mass \(500\; g\) rolls without slipping on a plane horizontal surface with its centre moving at a speed of \(5.00\; \mathrm{cm} / \mathrm{s}\). Its kinetic energy is

Consider a sample of oxygen behaving like an ideal gas. At \(300 \,K ,\) the ratio of root mean square (rms) velocity to the average velocity of gas molecule would be : (Molecular weight of oxygen is \(32 \,g / mol\) \(\left. R =8.3 \,J K ^{-1} mol ^{-1}\right)\)