A thin ring of \(10\, cm\) radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of \(40\,\pi \,rad\,{s^{ - 1}}\) about its axis, perpendicular to its plane. If the magnetic field at its centre is \(3.8 \times {10^{ - 9}}\,T\), then the charge carried by the ring is close to \(\left( {{\mu _0} = 4\pi  \times {{10}^{ - 7}}\,N/{A^2}} \right)\)

When a coil is placed in a time dependent magnetic field the power dissipated in it is \(P\). The number of turns, area of the coil and radius of the coil wire are \(N\), \(A\) and \(r\) respectively. For a second coils number of turns, area of the coil and radius of the coil wire are \(2N\), \(2A\) and \(3r\) respectively. When the first coil is replaced with second coil the power dissipated in it is \(\sqrt{2}\,\alpha P\). The value of \(\alpha\) is _______.

A particle \(A\) of mass \(‘m’\) and charge \(‘q’\) is accelerated by a potential difference of \(50\, V\). Another particle \(B\) of mass \(‘4\, m’\) and charge \(‘q’\) is accelerated by a potential difference of \(2500\, V\). The ratio of de-Broglie wavelength \(\frac{{{\lambda _A}}}{{{\lambda _B}}}\) is close to

Three particles of masses \(50\, g\), \(100\, g\) and \(150\, g\) are placed at the vertices of an equilateral triangle of side \(1\, m\) (as shown in the figure). The \((x, y)\) coordinates of the centre of mass will be

Match List-I with List-II.

List-I	List-II
(A) Isothermal	(I) \(\Delta W(\text{work done}) = 0\)
(B) Adiabatic	(II) \(\Delta Q(\text{supplied heat}) = 0\)
(C) Isobaric	(III) \(\Delta U(\text{change in internal energy}) \neq 0\)
(D) Isochoric	(IV) \(\Delta U = 0\)

Choose the correct answer from the options given below :

When light of frequency twice the threshold frequency is incident on the metal plate, the maximum velocity of emitted election is \(v _{1}\). When the frequency of incident radiation is increased to five times the threshold value, the maximum velocity of emitted electron becomes \(v _{2}\). If \(v _{2}= x\) \(v _{1}\), the value of \(x\) will be...........

Refer to the figure given below, current between terminals \(A\) and \(B\) is _____ A.

Two stars are \(10\) light years away from the earth. They are seen through a telescope of objective diameter \(30\, cm\). The wavelength of light is \(600\, nm\). To see the stars just resolved by the telescope, the minimum distance between them should be ( \(1\) light year \(= 9.46 \times 10^{15}\, m\)) of the order of

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:

When a hydrogen atom going from \(\mathrm{n}=2\) to \(\mathrm{n}=1\) emits a photon, its recoil speed is \(\frac{\mathrm{x}}{5} \mathrm{~m} / \mathrm{s}\). Where \(\mathrm{x}=\) _______. (Use : mass of hydrogen atom\(\left.=1.6 \times 10^{-27 /} \ \mathrm{kg}\right)\)

particle moves with simple harmonic motion in a straight line. In first \(\tau\ s\), after starting from rest it travels a distance \(a\), and in next \(\tau\ s\) it travels \(2a\), in same direction, then