A particle is moving in a circular path of radius \(a,\) with a constant velocity \(v\) as shown in the figure.The centre of circle is marked by \('C'\). The angular momentum from the origin \(O\) can be written as

A homogeneous solid cylindrical roller of radius \(R\) and mass \(M\) is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, angular acceleration of the cylinder is

The electric field of an electromagnetic wave travelling through a medium is given by \(\overline{E}(x,t) = 25\ sin(2.0 \times 10^{15}t - 10^{7}x)\hat{n}\) then the refractive index of the medium is ___________.
(All given measurement are in SI units)

Two ideal polyatomic gases at temperatures \(T _{1}\) and \(T _{2}\) are mixed so that there is no loss of energy. If \(F _{1}\) and \(F _{2}, m _{1}\) and \(m _{2}, n _{1}\) and \(n _{2}\) be the degrees of freedom, masses, number of molecules of the first and second gas respectively, the temperature of mixture of these two gases is

Consider two solid spheres of radii \(\mathrm{R}_{1}=1 \;\mathrm{m}\) \(\mathrm{R}_{2}=2\; \mathrm{m}\) and masses \(\mathrm{M}_{1}\) and \(\mathrm{M}_{2},\) respectively. The gravitational field due to sphere \((1)\) and \((2)\) are shown. The value of \(\frac{\mathrm{M}_{1}}{\mathrm{M}_{2}}\) is

The output of the given logic circuit is

Two gases-argon (atomic radius \(0.07 \;\mathrm{nm}\),atomic weight \(40\) ) and xenon (atomic radius \(0.1\; \mathrm{nm},\) atomic weight \(140\) ) have the same number density and are at the same temperature. The raito of their respective mean free times is closest to

Blocks of masses \(m , 2 m , 4 m\) and \(8 m\) are arranged in a line on a frictionless floor. Another block of mass \(m ,\) moving with speed \(v\) along the same line (see figure) ollides with mass \(m\) in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass \(8 m\) starts moving the total energy loss is \(p \%\) of the original energy. Value of \('p'\) is close to

In simple harmonic motion, the total mechanical energy of given system is E. If mass of oscillating particle \(P\) is doubled then the new energy of the system for same amplitude is _______.