Two particles, of masses \(M\) and \(2M\), moving as shown, with speeds of \(10\, m/s\) and \(5\, m/s\), collide elastically at the origin. After the collision, they move along the indicated directions with speeds \(v_1\) and \(v_2\) respectively. The value of \(v_1\) and \(v_2\) are nearly

An ideal gas has molecules with \(5\,\) degrees of freedom. The ratio of specific heats at constant pressure \((C_p)\) and at constant volume \((C_v)\) is

The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of inertia of a ring rotating in similar way. The moment of inertia of a solid sphere which has same radius as the disc and rotating in similar way, is \(n\) times higher than the moment of inertia of the given ring. Here, \(\mathrm{n}=\)_________
Consider all the bodies have equal masses.

A thin disc of mass \(M\) and radius \(R\) has mass per unit area \(\sigma (r) = kr^2\) where \(r\) is the distance from its centre. Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is

A Zener of breakdown voltage \(V_{z}=8\,V\) and maximum zener current, \(I _{ ZM }=10\,mA\) is subjected to an input voltage \(V _{ i }=10\,V\) with series resistance \(R=100\,\Omega\). In the given circuit \(R_{L}\) represents the variable load resistance. The ratio of maximum and minimum value of \(R_{L}\) is

A plane electromagnetic wave having a frequency \(n = 23.9\, GHz\) propagates along the positive \(z-\) direction in free space. The peak value of the electric field is \(60\, V/m\). Which among the following is the acceptable magnetic field component in the electromagnetic wave?

A progressive wave travelling along the positive \(x-\) direction is represented by \(y(x, t) = A\,sin\,\left( {kx - \omega t + \phi } \right)\). Its snapshot at \(t = 0\) is given in the figure For this wave, the phase \(\phi \) is

A thin infinite sheet charge and an infinite line charge of respective charge densities \(+\sigma\) and \(+\lambda\) are placed parallel at \(5\,m\) distance from each other. Points \(P\) and \(Q\), are at \(\frac{3}{\pi} m\) and \(\frac{4}{\pi} m\) perpendicular distance from line charge towards sheet charge, respectively. \(E_P\) and \(E_Q\) are the magnitudes of resultant electric field intensities at point \(P\) and \(Q\), respectively. If \(\frac{E_p}{E_Q}=\frac{4}{a}\) for \(2|\sigma|=|\lambda|\). Then the value of \(a\) is ...........

Match List \(I\) with List \(II\)

LIST \(I\)	LIST \(II\)
\(A\) Planck's constant \(( h )\)	\(I\) \(\left[ M ^1 L ^2 T ^{-2}\right]\)
\(B\) Stopping potential \(( Vs )\)	\(II\) \(\left[ M ^1 L ^1 T ^{-1}\right]\)
\(C\) Work function \((\phi)\)	\(III\) \(\left[ M ^1 L ^2 T ^{-1}\right]\)
\(D\) Momentum \(( p )\)	\(IV\) \(\left[ M ^1 L ^2 T ^{-3} A ^{-1}\right]\)

When \(5\ V\) potential difference is applied across a wire of length \(0.1\ m\), the drift speed of electrons is \(2.5 \times 10^{-4}\) \(ms^{-1}\) . If the electron density in the wire is \(8 \times 10^{28}\) \(m^{-3}\) the resistivity of the material is close to

A rod of length \(50\,cm\) is pivoted at one end. It is raised such that if makes an angle of \(30^o\) fro the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in \(rad\,s^{-1}\) ) will be \((g = 10\,ms^{-2})\)

Primary side of a transformer is connected to \(230 \mathrm{~V}, 50 \mathrm{~Hz}\) supply. Turns ratio of primary to secondary winding is \(10: 1\). Load resistance connected to secondary side is \(46\  \Omega\). The power consumed in it is :

A particle of mass \(\mathrm{m}\) is dropped from a height \(h\) above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of \(\sqrt{2 \mathrm{gh}} .\) If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of \(\sqrt{\frac{\mathrm{h}}{\mathrm{g}}}\) is