A solid steel ball of diameter 3.6 mm acquired terminal velocity \(2.45 \times 10^{-2} \mathrm{~m} / \mathrm{s}\) while falling under gravity through an oil of density \(925 \mathrm{~kg} \mathrm{~m}^{-3}\). Take density of steel as \(7825 \mathrm{~kg} \mathrm{~m}^{-3}\) and g as 9.8 \(\mathrm{m} / \mathrm{s}^2\). The viscosity of the oil in SI unit is

A ray of light passing through an equilateral prism is having velocity \(2.12 \times 10^8\) m/s in the prism material, then the minimum angle of deviation is _________ degrees.

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The density of the copper \(\left({ }_{29}^{64} \mathrm{Cu}\right)\) nucleus is greater than that of the carbon \(\left({ }_6^{12} \mathrm{C}\right)\) nucleus.
Reason (R): The nucleus of mass number A has a radius proportional to \(\mathrm{A}^{1 / 3}\).
In the light of the above statements, choose the most appropriate answer from the options given below :

The relative permittivity of distilled water is \(81 .\) The velocity of light in it will be \(....\,\times 10^{7}\,{m} / {s}\) \(\left(\right.\) Given \(\left.\mu_{r}=1\right)\)

How many alpha and beta particles are emitted when Uranium \({ }_{92} U ^{238}\) decays to lead \({ }_{82} Pb ^{206}\) ?

A stationary source emits sound waves of frequency \(500\, Hz\). Two observers moving along a line passing through the source detect sound to be of frequencies \(480\, Hz\) and \(530\, Hz\). Their respective speeds are, in \(m\,s^{-1}\) (Given speed of sound \(= 300\, m/s\))

An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet \(S\) having surface charge density \(+\sigma\). The electron at \(t=0\) is at a distance of 1 m from \(S\) and has a speed of \(1 m s ^{-1}\). The maximum value of \(\sigma\), if the electron strikes \(S\) at \(t=1 s\) is \(\alpha\left[\frac{m \epsilon_0}{e}\right] \frac{ C }{ m ^2}\). The value of \(\alpha\) is __________ .

If the earth suddenly shrinks to \(\frac{1}{64}\) th of its original volume with its mass remaining the same, the period of rotation of earth becomes \(\frac{24}{ x } h\). The value of \(x\) is \(.......\)

Two electrons each are fixed at a distance \('2d'\). A third charge proton placed at the midpoint is displaced slightly by a distance \(x ( x << d )\) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency : \(( m =\) mass of charged particle)

Three vectors \(\overrightarrow{\mathrm{OP}}, \overrightarrow{\mathrm{OQ}}\) and \(\overrightarrow{\mathrm{OR}}\) each of magnitude \(A\) are acting as shown in figure. The resultant of the three vectors is \(A \sqrt{x}\). The value of \(x\) is _______.

A copper wire of length \(1.0\, m\) and a steel wire of length \(0.5\, m\) having equal cross-sectional areas are joined end to end. The composite wire is stretched by a certain load which stretches the copper wire by \(1\, mm\). If the Young's modulii of copper and steel are respectively \(1.0\times10^{11}\, Nm^{-2}\) and \(2.0\times10^{11}\, Nm^{- 2}\), the total extension of the composite wire is ........ \(mm\)

Some distant star is to be observed by some telescope of diameter of objective lens \(a\), at an angular resolution of \(3.0\times 10^{-7}\) radian. If the wavelength of light from the star reaching the telescope is \(500\) nm, the minimum diameter of the objective lens of the telescope is ________ cm. (nearest integer)

A car is standing \(200\, m\) behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration \(2\,m/s^2\) and the car has acceleration \(4\, m/s^2\) . The car will catch up with the bus after a time of