The ratio of the shortest wavelength of Balmer series to the shortest wavelength of Lyman series for hydrogen atom is _______.

Your friend is having eye sight problem. She is not able lo see clearly a distant uniform window mesh and it appears to her as non-uniform and distorted. The doctor diagnosed the problem as

In an experiment for estimating the value of focal length of converging mirror, image of an object placed at \(40\,cm\) from the pole of the mirror is formed at distance \(120\,cm\) from the pole of the mirror. These distances are measured with a modified scale in which there are \(20\) small divisions in \(1\,cm\). The value of error in measurement of focal length of the mirror is \(1 / K\) \(cm\). The value of \(K\) is  \(..........\)

Statement \(I:\) If three forces \(\vec{F}_{1}, \vec{F}_{2}\) and \(\vec{F}_{3}\) are represented by three sides of a triangle and \(\overrightarrow{{F}}_{1}+\overrightarrow{{F}}_{2}=-\overrightarrow{{F}}_{3}\), then these three forces are concurrent forces and satisfy the condition for equilibrium. Statement \(II:\) A triangle made up of three forces \(\overrightarrow{{F}}_{1}, \overrightarrow{{F}}_{2}\) and \(\overrightarrow{{F}}_{3}\) as its sides taken in the same order, satisfy the condition for translatory equilibrium. In the light of the above statements, choose the most appropriate answer from the options given below:

In a plane \(EM\) wave, the electric field oscillates sinusoidally at a frequency of \(5 \times 10^{10} \mathrm{~Hz}\) and an amplitude of \(50 \mathrm{Vm}^{-1}\). The total average energy density of the electromagnetic field of the wave is _______. [Use \(\varepsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2\) ]

A stone of mass \(20\, {g}\) is projected from a rubber catapult of length \(0.1\, {m}\) and area of cross section \(10^{-6} \,{m}^{2}\) stretched by an amount \(0.04\, {m}\). The velocity of the projected stone is \(....\,m\,/s.\) (Young's modulus of rubber \(=0.5 \times 10^{9}\, {N} / {m}^{2}\) )

Moment of inertia of a body about a given axis is \(1.5\, kg\, m^2\) Initially the body is at rest. In order to produce a rotational kinetic energy of \(1200\, J\), the angular acceleration of \(20\, rad/s^2\) must be applied about the axis of rotation for a duration of ......... \(\sec\).

A body of mass \(5\,kg\) is moving with a momentum of \(10\,kg\,ms ^{-1}\). Now a force of \(2\,N\) acts on the body in the direction of its motion for \(5\,s\). The increase in the Kinetic energy of the body is \(...........J\).

The magnetic moments associated with two closely wound circular coils \(A\) and \(B\) of radius \(r_A=10 cm\) and \(r_B=20 cm\) respectively are equal if: (Where \(N _A, I _{ A }\) and \(N _B, I _{ B }\) are number of turn and current of \(A\) and \(B\) respectively)

There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at \(P\), in the region, is found to vary between in the limits \(589.0\,V\) to \(589.8\, V\). What is the potential at a point on the sphere whose radius vector makes an angle of \(60^o\) with the direction of the field ?........\(V\)

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 \(C\) )