A liquid column of height \(0.04 \mathrm{~cm}\) balances excess pressure of soap bubble of certain radius. If density of liquid is \(8 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}\) and surface tension of soap solution is \(0.28 \mathrm{Nm}^{-1}\), then diameter of the soap bubble is _______ \(\mathrm{cm}\). \(\text { (if } g=10 \mathrm{~ms}^{-2} \text { ) }\)

Consider a cylinder of mass \(M\) resting on a rough horizontal rug that is pulled out from under it with acceleration \('a'\) perpendicular to the axis of the cylinder. What is \(F_{friction}\) at point \(P\) ? It is assumed that the cylinder does not slip

The pitch and the number of divisions, on the circular scale, for a given screw gauge are \(0.5\,mm\) and \(100\) respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies \(3\) divisions below the mean line. The readings of the main scale and the circular scale for a thin sheet, are \(5.5\,mm\) and \(48\) respectively, the thickness of this sheet is

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

In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right of zero of the main scale and \(7^{\text{th}}\) Vernier division coincides with a main scale reading. If the value of \(1\) main scale division is \(1\) mm and there are \(10\) Vernier scale divisions, then the Vernier caliper has

An EM wave from air enters a medium. The electric fields are \(\overrightarrow {{E_1}}  = {E_{01}}\hat x\;cos\left[ {2\pi v\left( {\frac{z}{c} - t} \right)} \right]\) in air and \(\overrightarrow {{E_2}}  = {E_{02}}\hat x\;cos\left[ {k\left( {2z - ct} \right)} \right]\) in medium, where the wave number \(k\) and frequency \(v\) refer to their values in air. The medium is nonmagnetic. If \(\varepsilon {_{{r_1}}}\) and \(\varepsilon {_{{r_2}}}\) refer to relative permittivities of air and medium respectively, which of the following options is correct?

The surface charge density of a thin charged disc of radius \(R\) is \(\sigma \). The value of the electric field at the centre of the disc is \(\frac{\sigma }{{2\,{ \in _0}}}\). With respect to the field at the centre, the electric field along the axis at a distance \(R\) from the centre of the disc

In a series \(L R\) circuit \(X_{L}=R\) and power factor of the circuit is \(P _{1}\). When capacitor with capacitance \(C\) such that \(X _{ L }= X _{ C }\) is put in series, the power factor becomes \(P_{2}\). The ratio \(\frac{ P _{1}}{ P _{2}}\) is

The trajectory of a projectile in a vertical plane is \(y =\alpha x -\beta x ^{2},\) where \(\alpha\) and \(\beta\) are constants and \(x \& y\) are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection \(\theta\) and the maximum height attained \(H\) are respectively given by :-

\(200\,g\) water is heated from \(40\,^oC\) to \(60\,^oC.\) Ignoring the slight expansion of water, the change in its internal energy is close to ...... \(kJ\) (Given specific heat of water \(=4184\,J/kgK\) )

A capacitor of capacitance \(50 \; pF\) is charged by \(100 \; V\) source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the process is \(\dots \; nJ\).