A mass of $2 \mathrm{kg}$, initially at a height of $1.2 \mathrm{m}$ above an uncompressed spring with spring constant $2\times {10}^4 \mathrm{N} {\mathrm{m}}^{-1},$ is released from rest to fall on the spring. Taking the acceleration due to gravity as $10 \mathrm{m} {\mathrm{s}}^{-2}$ and neglecting the air resistance, the compression of the spring in $\mathrm{mm}$ is

A vessel contains hydrogen and nitrogen gases in the ratio \(2: 3\) by mass. If the temperature of the mixture of the gases is \(30^{\circ} \mathrm{C}\), then the ratio of the average kinetic energies per molecule of hydrogen and nitrogen gases is (Molecular mass of hydrogen \(=2\) and molecular mass of nitrogen \(=28\) )

Identify the correct option.

The effect due to uniform magnetic field on a freely suspended magnetic needle is as follows :

As shown in the figure, in a Wheatstone's bridge, three resistances \(\mathrm{P}, \mathrm{Q}\) and \(\mathrm{R}\) are connected in the three arms and the fourth arm is formed by two resistances \(S_1\) and \(S_2\) connected in parallel. The condition for the bridge to be balanced is

A wire of length, $l$ carries a current $I$ along the $X$- axis. The magnetic force acting on the wire is given by $\overrightarrow{F}=I{B}_{0}L(\hat{\mathrm{k}}-\hat{\mathrm{j}})\mathrm{T}$ where $B_0$ is a constant. The existing magnetic field $\overrightarrow{B}$ is

Ball $P$ of mass $m$ moving with velocity $\text{'}v\text{'}$ collides with another ball $Q$ of mass $2 \mathrm{m},$ at rest. If $v_P$ and $v_Q$ are the final velocities of $P$ and $Q$ respectively, after collision, then
(Assume the coefficient of restitution is $1/3$)

If the number of turns per unit length of a solenoid is doubled, what happens to the magnetic field in the solenoid?

Four identical masses of $m$ are kept at corners of a square. If the gravitational force exerted on one of masses by the other masses is $\left(\frac{2\sqrt{2}+1}{32}\right)\frac{G{m}^2}{{ L}^2},$ then the length of the side of the square is

A hydrogen sample is prepared in a particular excited state \(A\) of quantum number, \(n_A=3\). The ground state energy of hydrogen atom is \(-|E|\). The photons of energy \(\frac{|E|}{12}\) are absorbed in the sample which results in the excitation of some electrons to excited state \(B\) of quantum number \(n_B\), whose value is

Match the following table. \begin{array}{|c|c|c|c|} \hline & List-I & & List-II \ \hline A. & \begin{array}{l}\text { Michelson-Morley } \ \text { experiment }\end{array} & I. & \begin{array}{l}\text { The existence of } \ \text { anti-matter }\end{array} \ \hline B. & \begin{array}{l}\text { Stern-Gerlach } \ \text { experiment }\end{array} & II. & \begin{array}{l}\text { The existence of } \ \text { de-Broglie matter waves }\end{array} \ \hline C. & \begin{array}{l}\text { Davisson-Germer } \ \text { experiment }\end{array} & III. & Electrons have spins \ \hline D. & \begin{array}{l}\text { Anderson discovery } \ \text { of positron }\end{array} & \mathrm{IV}. & \begin{array}{l}\text { The non-existence of } \ \text { ether }\end{array} \ \hline \end{array} \(\begin{array}{llll}A & B & C & D\end{array}\)

A block of mass \(100 \mathrm{~g}\) is suspended vertically from a massless spring system of spring constant, \(k=1 \mathrm{~N} / \mathrm{m}\) each. The block is hit from above to impart an impulse of 2 Ns. Calculate the maximum displacement from the Equilibrium position of the block. (Take, \(g=10 \mathrm{~m} / \mathrm{s}^2\) )

Find the radius of \(\mathrm{Be}^{3+}\) ions in its ground state assuming Bohr's model to be valid \(\left(a_0=53 \mathrm{pm}\right)\).