Two satellite \(A\) and \(B\) go round a planet in circular orbits having radii \(4 R\) and \(R\) respectively. If the speed of \(\mathrm{A}\) is \(3 v\), the speed of \(\mathrm{B}\) will be _______.

A battery of \(6\,V\) is connected to the circuit as shown below. The current I drawn from the battery is:

The ratio of mass densities of nuclei of \(^{40}Ca\) and \(^{16}O\) is close to

A resistor dissipates \(192\, {J}\) of energy in \(1\, {s}\) when a current of \(4\, {A}\) is passed through it. Now, when the current is doubled, the amount of thermal energy dissipated in \(5 \,{s}\) in \(.....\,J.\)

The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth is closest to : [Boltzmans Constant \(k_B = 1.38\times10^{-23}\, J / K\) Avogadro number \(N_A = 6.02\times10^{26}\, / kg\) Radius of Earth \(: 6.4\times10^6\, m\) Gravitation acceleration on Earth \(= 10\, ms^{-2}\)]

The magnetic field in a plane electromagnetic wave is \(\mathrm{B}_y=\left(3.5 \times 10^{-7}\right) \sin \left(1.5 \times 10^3 \mathrm{x}+0.5\right.\) \(\left.\times 10^{11} \mathrm{t}\right) \mathrm{T}\). The corresponding electric field will be _______.

The gravitational field in a region is given by \(\vec E\) \(=(5\,N / kg)\, \hat i + (12\,N / kg)\,\hat j\) If the potential at the origin is taken to be zero, then the ratio of the potential at the points \((12\,m, 0)\) and \((0, 5\,m)\) is

As shown in the figure, a particle is moving with constant speed \(\pi\,m / s\). Considering its motion from \(A\) to \(B\), the magnitude of the average velocity is:

A vector \(\vec A \) is rotated by a small angle \(\Delta \theta\) radian \(( \Delta \theta << 1)\) to get a new vector \(\vec B\) In that case \(\left| {\vec B - \vec A} \right|\) is

A convex lens, of focal length \(30\,cm,\)  a concave lens of focal length \(120\,cm,\) and a plane mirror are arranged as shown. For an object kept at a distance of \(60\,cm\)  from the convex lens, the final image, formed by the combination, is a real image, at a distance of

If \(Y, K\) and \(\eta\) are the values of Young's modulus, bulk modulus and modulus of rigidity of any material respectively. Choose the correct relation for these parameters.

A plane electromagnetic wave of frequency 20 MHz travels in free space along the \(+x\) direction. At a particular point in space and time, the electric field vector of the wave is \(\mathrm{E}_y=9.3 \mathrm{Vm}^{-1}\). Then, the magnetic field vector of the wave at that point is: