If momentum \([ P ]\), area \([ A ]\) and time \([ T ]\) are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is :

A cyclotron is used to accelerate protons. If the operating magnetic field is \(1.0\,T\) and the radius of the cyclotron 'dees' is \(60 cm\), the kinetic energy of the accelerated protons in \(MeV\) will be. [use \(m _{p}=1.6 \times 10^{-27} kg , e =1.6 \times 10^{-19} C\) ]

Match List - I with List - II.

List - I	List - II
(A) Electric field inside (distance \(r>0\) from center) of a uniformly charged spherical shell with surface charge density \(\sigma\), and radius R.	(I) \(\sigma / \epsilon_0\)
(B) Electric field at distance \(r >0\) from a uniformly charged infinite plane sheet with surface charge density \(\sigma\).	(II) \(\sigma / 2 \epsilon_0\)
(C) Electric field outside (distance \(r>0\) from center) of a uniformly charged spherical shell with surface charge density \(\sigma\), and radius R.	(III) \(0\)
(D) Electric field between 2 oppositely charged infinite plane parallel sheets with uniform surface charge density \(\sigma\).	(IV) \(\frac{\sigma R^2}{\epsilon_0 r^2}\)

Choose the correct answer from the options given\(\text{ }\)below\(\text{ }\):

A block of mass \(2\,kg\) is attached with two identical springs of spring constant \(20\,N / m\) each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibrium position, it executes a simple harmonic motion. The time period of oscillation is \(\frac{\pi}{\sqrt{x}}\) in SI unit. The value of \(x\) is \(..........\)

The volume of an ideal gas increases 8 times and temperature becomes (1/4) of initial temperature during a reversible change. If there is no exchange of heat in this process (\( \Delta Q=0 \)) then identify the gas from the following options:

In a Young's double slit experiment, the width of the one of the slit is three times the other slit. The amplitude of the light coming from a slit is proportional to the slit-width. Find the ratio of the maximum to the minimum intensity in the interference pattern.

A steel rail of length \(5\,m\) and area of cross-section \(40\,cm^2\) is prevented from expanding along its length while the temperature rises by \(10\,^oC\). If coefficient of linear expansion and Young's modulus of steel are \(1.2\times10^{-5}\, K^{-1}\) and \(2\times10^{11}\, Nm^{-2}\) respectively, the force developed in the rail is approximately

A two point charges \(4 q\) and \(-q\) are fixed on the \(x-\)axis at \(x=-\frac{d}{2}\) and \(x=\frac{d}{2},\) respectively. If a third point charge \('q'\) is taken from the origin to \(x = d\) along the semicircle as shown in the figure, the energy of the charge will

Initially a gas of diatomic molecules is contained in a cylinder of volume \(V _{1}\) at a pressure \(P_{1}\) and temperature \(250\, K\). Assuming that \(25 \%\) of the molecules get dissociated causing a change in number of moles. The pressure of the resulting gas at temperature \(2000\, K ,\) when contained in a volume \(2 V _{1}\) is given by \(P _{2}\). The ratio \(\frac{P _{2}}{  P _{1}}\) is.

In an experiment to find \(emf\) of a cell using potentiometer, the length of null point for a cell of emf \(1.5\,V\) is found to be \(60\,cm\). If this cell is replaced by another cell of \(emf\; E\). the length-of null point increases by \(40\,cm\). The value of \(E\) is \(\frac{x}{10} V\). The value of \(x\) is \(............\)

A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is _______.

If momentum \((P),\) area \((A)\) and time \((T)\) are taken to be the fundamental quantities then the dimensional formula for energy is :

The half life period of radioactive element \({x}\) is same as the mean life time of another radioactive element \(y.\) Initially they have the same number of atoms. Then: