A water drop of radius \(1\,\mu m\) falls in a situation where the effect of buoyant force is negligible. Coefficient of viscosity of air is \(1.8 \times 10^{-5}\,Nsm ^{-2}\) and its density is negligible as compared to that of water \(10^{6}\,gm ^{-3}\). Terminal velocity of the water drop is________ \(\times 10^{-6}\,ms ^{-1}\) (Take acceleration due to gravity \(=10\,ms ^{-2}\) )

In a plane \(EM\) wave, the electric field oscillates sinusoidally at a frequency of \(5 \times 10^{10} \mathrm{~Hz}\) and an amplitude of \(50 \mathrm{Vm}^{-1}\). The total average energy density of the electromagnetic field of the wave is _______. [Use \(\varepsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2\) ]

\(100\) balls each of mass moving with speed \(v\) simultaneously strike a wall normally and reflected back with same speed, in time \(t s\). The total force exerted by the balls on the wall is

The energy band gap of semiconducting material to produce violet (wavelength \(=4000 \,A^{\circ}\) ) LED is \(.......eV\). (Round off to the nearest integer).

An air bubble of volume \(2.9 cm^3\) rises from the bottom of a swimming pool of 5 m deep. At the bottom of the pool water temperature is \(17^{\circ} C\). The volume of the bubble when it reaches the surface, where the water temperature is \(27^{\circ} C\), is ___________ \(cm ^3\). ( \(g =10 m / s ^2\), density of water \(=10^3 kg / m ^3\), and 1 atm pressure is \(10^5 Pa\) )

Two point charges \(q_1=3\,\mu C\) and \(q_2=-4\,\mu C\) are placed at points \((2\hat{i}+3\hat{j}+3\hat{k})\) and \((\hat{i}+\hat{j}+\hat{k})\) respectively. Force on charge \(q_2\) is ________ N. \(\left(\text{Take } \dfrac{1}{4\pi\epsilon_0} = 9\times 10^9 \text{ SI Units}\right)\)

In the following nuclear rection, \(D \stackrel{\alpha}{\longrightarrow} D _{1} \stackrel{\beta-}{\longrightarrow} D _{2} \stackrel{\alpha}{\longrightarrow} D _{3} \stackrel{\gamma}{\longrightarrow} D _{4}\) Mass number of \(D\) is \(182\) and atomic number is \(74\) . Mass number and atomic number of \(D _{4}\) respectively will be

In the experiment of \(Ohm's law,\) a potential difference of \(5.0\, V\) is applied across the end of a conductor of length \(10.0\, cm\) and diameter of \(5.00\, mm .\) The measured current in the conductor is \(2.00\, A\). The maximum permissible percentage error in the resistivity of the conductor is

A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field \(B =0.8\,T\). When released the radius of the loop starts shrinking at a constant rate of \(2\,cm ^{-1}\). The induced emf in the loop at an instant when the radius of the loop is \(10\,cm\) will be \(........mV\).

Statement \(I :\)Two forces \((\overrightarrow{{P}}+\overrightarrow{{Q}})\) and \((\overrightarrow{{P}}-\overrightarrow{{Q}})\) where \(\overrightarrow{{P}} \perp \overrightarrow{{Q}}\), when act at an angle \(\theta_{1}\) to each other, the magnitude of their resultant is \(\sqrt{3\left({P}^{2}+{Q}^{2}\right)}\), when they act at an angle \(\theta_{2}\), the magnitude of their resultant becomes \(\sqrt{2\left({P}^{2}+{Q}^{2}\right)}\). This is possible only when \(\theta_{1}<\theta_{2}\). Statement \(II :\) In the situation given above. \(\theta_{1}=60^{\circ} \text { and } \theta_{2}=90^{\circ}\) In the light of the above statements, choose the most appropriate answer from the options given below

A long straight wire of circular cross-section (radius \(a\)) is carrying steady current \(I\). The current \(I\) is uniformly distributed across this cross-section. The magnetic field is