A system of two blocks of masses \(m =2 \; kg\) and \(M=8 \; kg\) is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is \(0.5\). The maximum horizontal force \(F\) that can be applied to the block of mass \(M\) so that the blocks move together will be \(\dots \; N\)

A litre of dry air at \(STP\) expands adiabatically to a volume of \(3\) litres. If \(\gamma=1.40,\) the work done by air is\((3^{1.4}=4.6555)\) [Take air to be an ideal gas \(]\)

The radius of \(R\) of a nucleus of mass number \(A\) can be estimated by the formula \(R =\left(1.3 \times 10^{-15}\right) A ^{1 / 3}\, m .\) It follows that the mass density of a nucleus is of the order of \(\left( M _{\text {prot. }} \cong M _{\text {neut. }}=1.67 \times 10^{-27} kg \right)\)

The ratio of mass densities of nuclei of \(^{40}Ca\) and \(^{16}O\) is close to

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

List\(-I\) (Layer of atmosphere)	List\(-II\) (Approximate height over earth's surface)
\((A)\) \(F_1\) - Layer	\((I)\) \(10\,km\)
\((B)\) \(D-\) Layer	\((II)\) \(170-190\,km\)
\((C)\) Troposphere	\((III)\) \(100\,km\)
\((D)\) \(E-\)layer	\((IV)\) \(65-75\,km\)

Choose the correct answer from the options given below:

A solid conducting sphere, having a charge \(Q\), is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be \(V\). If the shell is now given a charge of \(-4\, Q\), the new potential difference between the same two surface is......\(V\)

A solid sphere of mass \(2\,kg\) is making pure rolling on a horizontal surface with kinetic energy \(2240\,J\). The velocity of centre of mass of the sphere will be \(..........ms ^{-1}\).

The dimensions of angular momentum , latent heat and capacitance are, respectively.

The temperature of a metal strip having coefficient of linear expansion \(\alpha\) is increased from \(T_1\) to \(T_2\) resulting in increase of its length by \(\Delta L_1\). The temperature is further increased from \(T_2\) to \(T_3\) such that the increase in its length is \(\Delta L_2\). Given \(T_3+T_1=2T_2\) and \(T_2-T_1=\Delta T\), the value of \(\Delta L_2\) is ______.

A wind-10.Powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed \(v\), the electrical 10.Power output will be most likely proportional to

Two waves executing simple harmonic motion travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the \(\sqrt{3}\) times of amplitude of individual motions. The phase difference between the two motions is \(.....(degree)\)

A person lives in a high-rise building on the bank of a river \(50\, m\) wide. Across the river is a well lit tower of height \(40\, m\). When the person, who is at a height of \(10\, m\), looks through a polarizer at an appropriate angle at light of the tower reflecting from the river surface, he notes that intensity of light coming from distance \(X\) from his building is the least and this corresponds to the light coming from light bulbs at height \('Y'\) on the tower. The values of \(X\) and \(Y\) are respectively close to (refractive index of water \(  \simeq  \frac{4}{3})\)