A body is moving in a low circular orbit about a planet of mass \(M\) and radius \(R\). The radius of the orbit can be taken to be \(R\) it self. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is

An \(HCl\) molecule has rotational, translational and vibrational motions. If the \(rms\) velocity of \(HCl\) molecules in its gaseous phase is \(\bar v ,\,m\) is its mass and \(k_B\) is Boltzmann constant, then its temperature will be

Four identical particles of mass \(m\) are kept at the four corners of a square. If the gravitational force exerted on one of the masses by the other masses is \(\left(\frac{2 \sqrt{2}+1}{32}\right) \frac{\mathrm{Gm}^2}{\mathrm{~L}^2}\), the length of the sides of the square is _______.

Mercury is filled in a tube of radius \(2 \mathrm{~cm}\) up to a height of \(30 \mathrm{~cm}\). The force exerted by mercury on the bottom of the tube is _______ \(\mathrm{N}\). (Given, atmospheric pressure \(=10^5 \mathrm{Nm}^{-2}\), density of mercury \(=1.36 \times 10^4 \mathrm{~kg} \mathrm{~m}^3, \mathrm{~g}=10 \mathrm{~ms}^2\), \(\left.\pi=\frac{22}{7}\right)\)

A potential barrier of \(0.4 \,V\) exists across a p-n junction. An electron enters the junction from the \(n\)-side with a speed of \(6.0 \times 10^{5} \,ms ^{-1}\). The speed with which electron enters the \(p\) side will be \(\frac{x}{3} \times 10^{5} \,ms ^{-1}\) the value of \(x\) is .............. (Given mass of electron \(=9 \times 10^{-31} \,kg\), charge on electron \(=1.6 \times 10^{-19} \,C\).)

The diameter of a spherical bob is measured using a vernier callipers. \(9\) divisions of the main scale, in the vernier callipers, are equal to \(10\) divisions of vernier scale. One main scale division is \(1\, {mm}\). The main scale reading is \(10\, {mm}\) and \(8^{\text {th }}\) division of vernier scale was found to coincide exactly with one of the main scale division. If the given vernier callipers has positive zero error of \(0.04\, {cm}\), then the radius of the bob is \(...... \,\times 10^{-2} \,{cm}\)

The angular width of the central maximum in a single slit diffraction pattern is \(60^o \) . The width of the slit is \(1\ \mu m\). The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young's fringes can be observed on a screen placed at  distance \(50\ cm\) from the slits. If the observed fringe width is \(1\ cm\), what is slit separation distance?.........\(\mu m\)
(i.e. distance between the centres of each slit. )

Two cells of same emf but different internal resistances \(I_{1}\) and \(I_{2}\) are connected in series with a resistance \(R\). The value of resistance \(R\), for which the potential difference across second cell is zero, is

A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by \(y\left( {x,t} \right) = 0.5\sin\, \left( {\frac{{5\pi }}{4}x} \right)\,\cos\, \left( {200\,\pi t} \right)\). What is the speed of the travelling wave moving in the positive \(x\) direction .... \(m/s\) ? (\(x\) and \(t\) are in meter and second, respectively.)

A string of length \(L\) is fixed at one end and carries a mass of \(M\) at the other end. The mass makes \(\left(\frac{3}{\pi}\right)\) rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is \(\ldots\ldots\) ML.

A circuit is arranged as shown in figure. The output voltage \({V}_{0}\) is equal to \(\ldots \ldots . {V}\).

The balancing length for a cell is \(560 \;\mathrm{cm}\) in a potentiometer experiment. When an external resistance of \(10 \;\Omega\) is connected in parallel to the cell, the balancing length changes by \(60\; \mathrm{cm} .\) If the internal resistance of the cell is \(\frac{\mathrm{N}}{10} \;\Omega,\) where \(\mathrm{N}\) is an integer then value of \(\mathrm{N}\) is

Sodium light of wavelengths \(650\, nm\) and \(655\, nm\) is used to study diffraction at a single slit of aperture \(0.5\, mm\). The distance between the slit and the screen is \(2.0 \,m\). The separation between the positions of the first maxima of diffraction pattern obtained in the two cases is \(\times 10^{-5} \,m\)