A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength \(980\,\mathop A\limits^o \). The radius of the atom in the excited state, in  terms of Bohr radius \(a_0,\) will be \((hc\,=\,12500\,eV-\mathop A\limits^o)\)

Two charges each of magnitude \(0.01\,C\) and separated by a distance of \(0.4\,mm\) constitute an electric dipole. If the dipole is placed in an uniform electric field ' \(\vec{E}\) ' of \(10\,dyne/C\) making \(30^{\circ}\) angle with \(\overrightarrow{ E }\), the magnitude of torque acting on dipole is :

Match List\(-I\) with List\(-II\) 

List\(-I\)	List\(-II\)
\((A)\) \(AC\) generator	\((I)\) Detects the presence of current in the circuit
\((B)\) Galvanometer	\((II)\) Converts mechanical energy into electrical energy
\((C)\) Transformer	\((III)\) Works on the principle of resonance in \(AC\) circuit
\((D)\) Metal detector	\((IV)\) Changes an alternating voltage for smaller or greater value

Choose the correct answer from the options given below

A huge circular arc of length \(4.4\) \(ly\) subtends an angle \('4 {s}'\) at the centre of the circle. How long it would take for a body to complete \(4\) revolution if its speed is \(8 \;AU\;per\, second \;?\) Given : \(1\, {ly}=9.46 \times 10^{15} \,{m},\) \(\, {AU}=1.5 \times 10^{11}\, {m}\)

A closed organ and an open organ tube are filled by two different gases having same bulk modulus but different densities \(\rho_1\) and \(\rho_{2^{\prime}}\), respectively. The frequency of \(9^{\text {th }}\) harmonic of closed tube is identical with \(4^{\text {th }}\) harmonic of open tube. If the length of the closed tube is 10 cm and the density ratio of the gases is \(\rho_1: \rho_2=1: 16\), then the length of the open tube is :

Two resistors of \(100 \Omega\) each are connected in series with a 9 V battery. A voltmeter of \(400 \Omega\) resistance is connected to measure the voltage drop across one of the resistors. The voltmeter reading is _________ V.

A tightly wound long solenoid carries a current of 1.5 A . An electron is executing uniform circular motion inside the solenoid with a time period of 75 ns . The number of turns per metre in the solenoid is ________.
[Take mass of electron \(\mathrm{m}_{\mathrm{e}}=9 \times 10^{-31} \mathrm{~kg}\), charge of electron \(\left|\mathrm{q}_{\mathrm{e}}\right|=1.6 \times 10^{-19} \mathrm{C}\),
\(\left.\mu_0=4 \pi \times 10^{-7} \frac{\mathrm{~N}}{\mathrm{~A}^2}, 1 \mathrm{~ns}=10^{-9} \mathrm{~s}\right]\)

A small spherical ball of radius \(0.1 \,mm\) and density \(10^{4} \,kg m ^{-3}\) falls freely under gravity through a a distance \(h\) before entering a tank of water. If after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value of \(h\) wil be \(m\). (Given \(g =10 \,ms ^{-2}\), viscosity of water \(=1.0 \times 10^{-5} \,N - sm ^{-2}\) )

The number density of free electrons in copper is nearly \(8 \times 10^{28}\,m ^{-3} . A\) copper wire has its area of cross section \(=2 \times 10^{-6}\,m ^2\) and is carrying a current of \(3.2\,A\). The drift speed of the electrons is \(.....\times 10^{-6}\,ms ^{-1}\).

A straight rod of length \(L\) extends from \(x = a\) to \(x = L + a\). The gravitational force it exerts on a point mass \(‘m’\) at \(x = 0\), if the mass per unit length of the rod is \(A + Bx^2\), is given by

An \(\alpha\) particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particals will be.

Consider two blocks A and B of masses \(m_1=10 \mathrm{~kg}\) and \(m_2=5 \mathrm{~kg}\) that are placed on a frictionless table. The block A moves with a constant speed \(v=3 \mathrm{~m} / \mathrm{s}\) towards the block B kept at rest. A spring with spring constant \(\mathrm{k}=3000 \mathrm{~N} / \mathrm{m}\) is attached with the block B as shown in the figure. After the collision, suppose that the blocks A and B, along with the spring in constant compression state, move together, then the compression in the spring is _______. (Neglect the mass of the spring)