In Millikan's oil drop experiment, what is viscous force acting on an uncharged drop of radius \(2.0 \times 10^{-5}\, {m}\) and density \(1.2 \times 10^{3} \,{kgm}^{-3}\) ? Take viscosity of liquid \(=1.8 \times 10^{-5}\, {Nsm}^{-2} .\) (Neglect buoyancy due to air).

Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure

A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s . The EMF induced in the loop is ___________ mV.

A \(90 \mathrm{~kg}\) body placed at \(2 \mathrm{R}\) distance from surface of earth experiences gravitational pull of _______. ( \(\mathrm{R}=\) Radius of earth, \(\mathrm{g}=10 \mathrm{~ms}^{-2}\) )

Two known resistance of \(R \Omega\) and \(2 R \Omega\) and and one unknown resistance \(X \Omega\) are connected in a circuit as shown in the figure. If the equivalent resistance between points A and B in the circuit is \(X \Omega\), then the value of X is _________ \(\Omega\).

A block of mass \(10\, kg\) starts sliding on a surface with an initial velocity of \(9.8\, ms ^{-1}\). The coefficient of friction between the surface and bock is \(0.5\). The distance covered by the block before coming to rest is: [use \(g =9.8\, ms ^{-2}\) ].........\(m\)

10 kg of ice at \(-10^{\circ}C\) is added to 100 kg of water to lower its temperature from \(25^{\circ}C.\) Consider no heat exchange to surroundings. The decrement to the temperature of water is ___________ \(^{\circ}C.\)
(specific heat of ice \(= 2100\ J/Kg.^{\circ}C\), specific heat of water \(= 4200\ J/Kg.^{\circ}C\), latent heat of fusion of ice \(= 3.36 \times 10^{5}\ J/Kg\))

Two projectile thrown at \(30^{\circ}\) and \(45^{\circ}\) with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is

An electric dipole has a fixed dipole moment \(\vec P\) which makes angle \(\theta \) with respect to \(x-\)axis. When subjected to an electric field \(\overrightarrow {{E_1}} \) \(=E\)\(\hat i\) it experiences a torque \(\overrightarrow {{T_1}} \) =\(\;\tau \hat k\) When subjected to another electric field \(\overrightarrow {{E_2}}  = \sqrt 3 {E_1}\hat j\) it experiences torque \(\overrightarrow {{T_2}} \) = \( - \overrightarrow {{T_1}} \) The angle \(\theta \;\) is.......\(^o\)

The potential (in volts ) of a charge distribution is given by \(V(z)\, = \,30 - 5{z^2}for\,\left| z \right| \le 1\,m\) \(V(z)\, = \,35 - 10\,\left| z \right|for\,\left| z \right| \ge 1\,m\) \(V(z)\)  does not depend on \(x\)  and  \(y.\)  If this potential is generated by a constant charge per unit volume \(\rho _0\) (in units of \(\varepsilon _0\) ) which is spread over a certain region, then choose the correct statement

According to Bohr's theory, the moment of momentum of an electron revolving in \(4^{\text {th }}\) orbit of hydrogen atom is _______.

In the equation \(\left[X+\frac{a}{Y^2}\right][Y-b]= R T, X\) is pressure, \(Y\) is volume, \(R\) is universal gas constant and \(T\) is temperature. The physical quantity equivalent to the ratio \(\frac{a}{b}\) is

When the position vector \(\overrightarrow{ r }=x \hat{ i }+y \hat{ j }+z \hat{ k }\) changes sign as \(-\overrightarrow{ r }\), which one of the following vector will not flip under sign change ?