An oil drop of radius \(2\, mm\) with a density \(3\, g\) \(cm ^{-3}\) is held stationary under a constant electric field \(3.55 \times 10^{5}\, V\, m ^{-1}\) in the Millikan's oil drop experiment. What is the number of excess electrons that the oil drop will possess ? (consider \(\left. g =9.81\, m / s ^{2}\right)\)

In thermodynamics, heat and work are

For a free body diagram shown in the figure, the four forces are applied in the ' \(x\) ' and ' \(y\) ' directions. What additional force must be applied and at what angle with positive \(x\)-axis so that the net acceleration of body is zero?

A sample of gas expands from \(V_1\) to \(V _2\). In which of the following, the work done will be greatest ?

A thin circular disc is in the \(xy\) plane as shown in the figure. The ratio of its moment of inertia about \(z\)  and \(z'\)  axes will be

The displacement x versus time graph is shown below.

(A) The average velocity during 0 to 3 s is \(10 \mathrm{~m} / \mathrm{s}\)
(B) The average velocity during 3 to 5 s is \(0 \mathrm{~m} / \mathrm{s}\)
(C) The instantaneous velocity at \(\mathrm{t}=2 \mathrm{~s}\) is \(5 \mathrm{~m} / \mathrm{s}\)
(D) The average velocity during 5 to 7 s and instantaneous velocity at \(\mathrm{t}=6.5 \mathrm{~s}\) are equal
(E) The average velocity from \(t=0\) to \(t=9 \mathrm{~s}\) is zero
Choose the correct answer from the options given below:

When you walk through a metal detector carrying a metal object in your pocket, it raises an alarm. This phenomenon works on

An electromagnetic wave of frequency \(5\, GHz ,\) is travelling in a medium whose relative electric permittivity and relative magnetic permeability both are \(2 .\) Its velocity in this medium is \(\times 10^{7}\, m / s\)

Suppose you have taken a dilute solution of oleic acid in such a way that its concentration becomes \(0.01 \,cm ^{3}\) of oleic acid per \(cm ^{3}\) of the solution. Then you make a thin film of this solution (monomolecular thickness) of area \(4\, cm ^{2}\) by considering \(100\) spherical drops of radius \(\left(\frac{3}{40 \pi}\right)^{\frac{1}{3}} \times 10^{-3}\, cm .\) Then the thickness of oleic acid layer will be \(x \times 10^{-14} \,m\). Where \(x\) is ...... .

Nearly \(10 \%\) of the power of a \(110\,W\) light bulb is converted to visible radiation. The change in average intensities of visible radiation, at a distance of \(1\, m\) from the bulb to a distance of \(5\,m\) is \(a \times 10^{-2}\,W / m ^{2}\). The value of ' \(a\) ' will be.

A cyclotron is used to accelerate protons. If the operating magnetic field is \(1.0\,T\) and the radius of the cyclotron 'dees' is \(60 cm\), the kinetic energy of the accelerated protons in \(MeV\) will be. [use \(m _{p}=1.6 \times 10^{-27} kg , e =1.6 \times 10^{-19} C\) ]

Consider two containers \(A\) and \(B\) containing monoatomic gases at the same Pressure \((P)\), Volume \((V)\) and Temperature \((T)\). The gas in \(A\) is compressed isothermally to \(\frac{1}{8}\) of its original volume while the gas \(B\) is compressed adiabatically to \(\frac{1}{8}\) of its original volume. The ratio of final pressure of gas in \(B\) to that of gas in \(A\) is ...........