Figure shows charge \((q)\) versus voltage \((V)\) graph for series and parallel combination of to given capacitors. The capacitances are

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 \(10^5 Pa\) )

A diverging lens with magnitude of focal length \(25\ cm\) is placed at a distance of \(15\ cm\) from a converging lens of magnitude of focal length \(20\ cm\). A beam of parallel light falls on the diverging lens. The final image formed is

Two capacitors having capacitance \(C _{1}\) and \(C _{2}\) respectively are connected as shown in figure. Initially, capacitor \(C _{1}\) is charged to a potential difference \(V\) volt by a battery. The battery is then removed and the charged capacitor \(C_{1}\) is now connected to uncharged capacitor \(C _{2}\) by closing the switch \(S\). The amount of charge on the capacitor \(C _{2}\), after equilibrium is

The time period of a satellite revolving around earth in a given orbit is \(7 \,hours\). If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be ...... \(hours\)

If the potential energy between two molecules is given by \(U =\frac{-A }{ r ^{6}}+\frac{ B }{ r ^{12}},\) then at equilibrium, separation between molecules, and the potential energy are

A uniform cylinder of length \(L\) and mass \(M\) having crosssectional area \(A\) is suspended, with its length vertical, from a fixed point by a massless spring such that it is half submerged in a liquid of density \(\sigma\) at equilibrium position. The extension \(x_0\) of the spring when it is in equilibrium is

One mole of an ideal gas is taken through an adiabatic process where the temperature rises from \(27^{\circ} {C}\) to \(37^{\circ} {C}\). If the ideal gas is composed of polyatomic molecule that has \(4\) vibrational modes which of the following is true?

A uniform electric field \(\vec E\) exists between the plates of a charged condenser. A charged particle enters the space between the plates and perpendicular to \(\vec E\) . The path of the particle between the plates is a

A plane electromagnetic wave of frequency \(25\; \mathrm{GHz}\) is propagating in vacuum along the \(z-\)direction. At a particular point in space and time, the magnetic field is given by \(\overrightarrow{\mathrm{B}}=5 \times 10^{-8} \hat{\mathrm{j}}\; \mathrm{T}\). The corresponding electric field \(\overrightarrow{\mathrm{E}}\) is (speed of light  \(\mathrm{c}=3 \times 10^{8}\; \mathrm{ms}^{-1})\)

Two long parallel wires carrying currents \(8\,A\) and \(15\,A\) in opposite directions are placed at a distance of \(7\,cm\) from each other. A point \(P\) is at equidistant from both the wires such that the lines joining the point \(P\) to the wires are perpendicular to each other. The magnitude of magnetic field at \(P\) is \(............\times 10^{-6}\,T\). (Given : \(\left.\sqrt{2}=1.4\right)\)

An alternating \(emf\) \(E =440 \sin 100 \pi t\) is applited to a circuit containing an inductance of \(\frac{\sqrt{2}}{\pi} H\). If an a.c. ammeter is connected in the circuit, its reading will be \(.......A\)