A hollow metal sphere of radius \(15 \mathrm{~cm}\) is charged such that potential on its surface is \(20 \mathrm{~V}\). Then, the potential at the centre of sphere is

If \(\mathrm{S}\) is the surface area of a nucleus of mass number \(\mathrm{A}\), th en

A laser beam has intensity $17.7\times {10}^{14} \mathrm{W}/{\mathrm{m}}^2.$ The amplitude of the electric field is
[Use ${\epsilon }_0=8.85\times {10}^{-12}\frac{C^2}{N-M^2}$]

Gravitational forces operate among which of the following?

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 particle is moving along the \(Y\)-axis. The position of the particle from the origin as a function of time \((t)\) is given as \(y(t)=10 t e^{-2 t}\). How far is the particle from the origin when it stops momentarily? ( \(y\) is given in units of metre and \(t\) is in units of second)

A drone fitted with siren in flying directly away from the drone operator and towards a distant building at a speed of \(15 \mathrm{~m} / \mathrm{s}\). The siren produces sound of frequency \(780 \mathrm{~Hz}\). What is the frequency that the operator hears in the echo reflected from the building. [Speed of sound is \(340 \mathrm{~m} / \mathrm{s}\).]

In a plane EM wave the electric field oscillates sinusoidally at a frequency of \(30 \mathrm{MHz}\) and amplitude \(150 \mathrm{~V} / \mathrm{m}\). Identify the correct expression of \(\overline{\mathrm{B}}\) assuming the wave is propagating along \(x\)-axis and is oscillating along \(y\)-axis.

Young's modulus is proportionality constant that relates the force per unit area applied perpendicularly at the surface of an object to

Three long, straight, parallel wires carrying different currents are arranged as shown in the diagram. In the given arrangement, let the net force per unit length on the wire ' \(C\) ' be \(\vec{F}\). If the wire ' \(B\) ' is removed without disturbing the other two wires, then the force per unit length on wire ' \(\mathrm{A}\) ' is

A projectile object is thrown in the upward direction making an angle of \(60^{\circ}\) with the horizontal with velocity of \(140 \mathrm{~m} / \mathrm{s}\). Then, the time after which its velocity makes an angle \(30^{\circ}\) with the horizontal is (Take, \(g=10 \mathrm{~m} / \mathrm{s}^2\) )

A body travels in a straight line from point \(A\) to point \(B\) with an initial velocity zero and uniform acceleration, covering \(1 \mathrm{~m}\) during the first second and \(39 \mathrm{~m}\) during the last second. The distance between \(A\) and \(B\) in metre is

The ratio of maximum to minimum wavelength in Balmer series of an hydrogenic atom is