A satellite is launched into a circular orbit of radius \(‘R’\) around earth while a second satellite is launched into an orbit of radius \(1.02 R\). The percentage difference in the time periods of the two satellites is ......... \(\%\)

A body starts falling freely from height \(\mathrm{H}\) hits an inclined plane in its path at height \(\mathrm{h}\). As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of \(\frac{\mathrm{H}}{\mathrm{h}}\) for which the body will take the maximum time to reach the ground is _______.

From the circuit given below, the capacitance between terminals \(A\) and \(B\) shown in the circuit is ______ \(\mu\)F.
(take \(C_1=C_2=C_3=1\) \(\mu\)F and \(C_4=2\) \(\mu\)F.)

Space between the plates of a parallel plate capacitor of plate area \(4 \mathrm{~cm}^2\) and separation of (d) 1.77 mm, is filled with uniform dielectric materials with dielectric constants (3 and 5) as shown in figure. Another capacitor of capacitance 7.5 pF is connected in parallel with it. The effective capacitance of this combination is ________ pF. \(\left(\right.\) Given \(\left.\varepsilon_0=8.85 \times 10^{-12} \mathrm{~F} / \mathrm{m}\right)\)

\(1\,g\) of a liquid is converted to vapour at \(3 \times 10^5\,Pa\) pressure. If \(10 \%\) of the heat supplied is used for increasing the volume by \(1600\,cm ^3\) during this phase change, then the increase in internal energy in the process will be \(............\,J\)

An elastic spring under tension of \(3 \mathrm{~N}\) has a lengtha. Its length is \(b\) under tension \(2 \mathrm{~N}\). For its length\((3 a-2 b)\), the value of tension will be_______. \(\mathrm{N}\).

As shown in the figure, a network of resistors is connected to a battery of \(2\,V\) with an internal resistance of \(3\,\Omega\). The currents through the resistors \(R_4\) and \(R_5\) are \(I_4\) and \(I_5\) respectively. The values of \(I_4\) and \(I_5\) are :

A force of \(10 \; N\) acts on a charged particle placed between two plates of a charged capacitor. If one plate of capacitor is removed, then the force acting on that particle will be ...... \(N\)

A piece of wood of mass \(0.03\, kg\) is dropped from the top of a \(100\, m\) height building. At the same time, a bullet of mass \(0.02\, kg\) is fired vertically upward, with a velocity \(100\, ms^{- 1}\), from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is ........ \(m\). \((g = 10\, ms^{-2})\)

The percentage decrease in the weight of a rocket, when taken to a height of \(32 km\) above the surface of earth will, be\(.....\%\) (Radius of earth \(=6400\,km\) )

Consider two separate ideal gases of electrons and protons having same number of particles. The temperature of both the gases are same. The ratio of the uncertainty in determining the position of an electron to that of a proton is proportional to :-

Two long parallel conductors \(S_{1}\) and \(S_{2}\) are separated by a distance \(10 \,cm\) and carrying currents of \(4\, A\) and \(2 \,A\) respectively. The conductors are placed along \(x\)-axis in \(X - Y\) plane. There is a point \(P\) located between the conductors (as shown in figure). A charge particle of \(3 \pi\) coulomb is passing through the point \(P\) with velocity \(\overrightarrow{ v }=(2 \hat{ i }+3 \hat{ j }) \,m / s\); where \(\hat{i}\) and \(\hat{j} \quad\) represents unit vector along \(x\) and \(y\) axis respectively. The force acting on the charge particle is \(4 \pi \times 10^{-5}(-x \hat{i}+2 \hat{j}) \,N\). The value of \(x\) is