A body weights \(49\,N\) on a spring balance at the north pole. ..... \(N\) will be its weight recorded on the same weighing machine, if it is shifted to the equator? (Use \(g=\frac{G M}{R^{2}}=9.8 \,ms ^{-2}\) and radius of earth, \(R =6400\, km .]\)

Two different wires having lengths \(L _{1}\) and \(L _{2}\) and respective temperature coefficient of linear expansion \(\alpha_{1}\) and \(\alpha_{2},\) are joined end-to-end. Then the effective temperature coefficient of linear expansion is

The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths, \(\lambda _1/\lambda _2\), of the photons emitted in this process is

The half life period of a radioactive substance is 60 days. The time taken for \(\frac{7}{8}\) th of its original mass to disintegrate will be \(......days\) 

From the given transfer characteristic of a transistor in \(CE\) configuration, the value of power gain of this configuration is \(10^{ x }\), for \(R_B=10\,k \Omega\), and \(R _C=1\,k \Omega\). The value of \(x\) is \(.....\).

Consider an electron in a hydrogen atom, revolving in its second excited state (having radius \(4.65\, \mathop A\limits^o \)). The de-Broglie wavelength of this electron is....\(\mathop A\limits^o \)

In the given circuit, value of \(Y\) is

A bullet of mass \(10\, g\) and speed \(500\, m/s\) is fired into a door and gets embedded exactly at the centre of the door. The door is \(1.0\, m\) wide and weighs \(12\, kg\). It is hinged at one end and rotates about a vertical axis practically without friction . The angular speed of the door just after the bullet embeds into it will be

Experimentally it is found that \(12.8\,eV\) energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is \(\frac{9}{ x } \times 10^{-10}\,m\). The value of the \(x\) is \(\left(1\,eV =1.6 \times 10^{-19}\,J , \frac{1}{4 \pi \epsilon_0}=9 \times 10^9\,Nm ^2 / C ^2\right.\) and electronic charge \(=1.6 \times 10^{-19}\,J\,C\) )

If a wave gets refracted into a denser medium, then which of the following is true?

Two charges \(7 \mu C\) and \(-2 \mu C\) are placed at \((-9,0,0) cm\) and \((9,0,0) cm\) respectively in an external field \(E=\frac{ A }{ r ^2} \hat{ r }\), where \(A=9 \times 10^5 N / C . m ^2\).
Considering the potential at infinity is 0 , the electrostatic energy of the configuration is ___________ J .

The translational degrees of freedom \((f)\) and rotational degrees of freedom \((f)\) of \(\mathrm{CH}_4\) molecule are _______.

The escape velocities of two planets \(A\) and \(B\) are in the ratio \(1: 2\). If the ratio of their radii respectively is \(1: 3\), then the ratio of acceleration due to gravity of planet \(A\) to the acceleration of gravity of planet \(B\) will be: