A light unstretchable string passing over a smooth light pulley connects two blocks of masses \(m_1\) and \(m_2\). If the acceleration of the system is \(\frac{g}{8}\), then the ratio of the masses \(\frac{\mathrm{m}_2}{\mathrm{~m}_1}\) is _______.

When \(5\ V\) potential difference is applied across a wire of length \(0.1\ m\), the drift speed of electrons is \(2.5 \times 10^{-4}\) \(ms^{-1}\) . If the electron density in the wire is \(8 \times 10^{28}\) \(m^{-3}\) the resistivity of the material is close to

A litre of dry air at \(STP\) expands adiabatically to a volume of \(3\) litres. If \(\gamma=1.40,\) the work done by air is\((3^{1.4}=4.6555)\) [Take air to be an ideal gas \(]\)

The electric potential at the centre of two concentric half rings of radii \(R_1\) and \(R_2\), having same linear charge density \(\lambda\) is

The de-Broglie wavelength associated with the electron in the \(n\, = 4\) level is

In the cube of side \(a\) shown in the figure, the vector from the central point of the face \(ABOD\) to the central point of the face \(BEFO\) will be

Two wires each of radius \(0.2\,cm\) and negligible mass, one made of steel and other made of brass are loaded as shown in the figure. The elongation of the steel wire is \(.........\times 10^{-6}\,m\). [Young's modulus for steel \(=2 \times 10^{11}\,Nm ^{-2}\) and \(g =10\,ms ^{-2}\) ]

Figure shows charge \((q)\) versus voltage \((V)\) graph for series and parallel combination of to given capacitors. The capacitances are

A capacitor has air as dielectric medium and two conducting plates of area \(12 \mathrm{~cm}^2\) and they are \(0.6 \mathrm{~cm}\) apart. When a slab of dielectric having area \(12 \mathrm{~cm}^2\) and \(0.6 \mathrm{~cm}\) thickness is inserted between the plates, one of the conducting plates has to be moved by \(0.2 \mathrm{~cm}\) to keep the capacitance same as in previous case. The dielectric constant of the slab is _______. (Given \(\left.\epsilon_0=8.834 \times 10^{-12} \mathrm{~F} / \mathrm{m}\right)\)

Match List-I with List-II.

List-I	List-II
A. Meter (L)	I. \(\sqrt{\dfrac{hc}{G}}\)
B. Second (S)	II. \(\sqrt{\dfrac{Gh}{c^5}}\)
C. Kilogram (M)	III. \(\sqrt{\dfrac{K^2L^2c^3}{Gh}}\)
D. Kelvin (K)	IV. \(\sqrt{\dfrac{Gh}{c^3}}\)

where \(h\) (Planck's constant), \(G\) (gravitational constant) and \(c\) (speed of light in vacuum) as fundamental units.
Choose the correct answer from the options given below :

A person has been using spectacles of power- \(1.0\) diopter for distant vision and a separate reading glass of power \(2.0\) diopters. What is the least distance of distinct vision for this person \(.......cm\)