The radius of curvature of each surface of a convex lens having refractive index \(1.8\) is \(20\,cm\). The lens is now immersed in a liquid of refractive index \(1.5\). The ratio of power of lens in air to its power in the liquid will be \(x : 1\). The value of \(x\) is \(.....\)

The magnifying power of a telescope with tube \(60\; \mathrm{cm}\) is \(5 .\) What is the focal length of its eye piece?......\(cm\)

A particle of mass \(m\) is moving in a circular path of constant radius \(I\) such that its centripetal acceleration \((a)\) is varying with time \(t\) as \(a=k^{2} rt^{2}\). where \(k\) is a constant. The 10.Power delivered to the particle by the force acting on it is given as

A bi convex lens of focal length \(10\,cm\) is cut in two identical parts along a plane perpendicular to the principal axis. The power of each lens after cut is \(...........\,D\).

Orbits of a particle moving in a circle are such that the perimeter of the orbit equals an integer number of de-Broglie wavelengths of the particle. For a charged particle moving in a plane perpendicular to a magnetic field, the radius of the \(n^{th}\) orbital will therefore be proportional to

A paramagnetic substance in the form of a cube with sides \(1\, cm\) has a magnetic dipole moment of \(20 \times 10^{-6}\, J/T\) when a magnetic intensity of \(60 \times 10^3\, A/m\) is applied. Its magnetic susceptibility is

Two identical positive charges \(Q\) each are fixed at a distance of ' \(2 a\) ' apart from each other. Another point charge qo with mass ' \(m\) ' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge \(q_{0}\) executes \(SHM\). The time period of oscillation of charge \(q_{0}\) will be.

A galvanometer coil has \(500\) turns and each turn has an average area of \(3 \times 10^{-4}\, m ^{2}\). If a torque of \(1.5\,Nm\) is required to keep this coil parallel to magnetic field when a current of \(0.5\, A\) is flowing through it, the strength of the field (in \(T )\) is

In \(LC\) circuit the inductance \(\mathrm{L}=40\; \mathrm{mH}\) and capacitance \(\mathrm{C}=100\; \mu \mathrm{F} .\) If a voltage \(\mathrm{V}(\mathrm{t})=10 \sin (314 \mathrm{t})\) is applied to the circuit, the current in the circuit is given as 

The dipole moment of a circular loop carrying a current \(I\), is \(m\) and the magnetic field at the centre of the loop is \(B_1\) . When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is \(B_2\) . The ratio \(\frac{{{B_1}}}{{{B_2}}}\) is

In a double slit experiment the distance between the slits is 0.1 cm and the screen is placed at 50 cm from the slits plane. When one slit is covered with a transparent sheet having thickness \(t\) and refractive index \(n (=1.5)\), the central fringe shifts by 0.2 cm . The value of t is _________ cm .