The amount of heat needed to raise the temperature of \(4\, moles\) of a rigid diatomic gas from \(0^{\circ} {C}\) to \(50^{\circ} {C}\) when no work is done is ......\({R}\) (\(R\) is the universal gas constant)

A diatomic gas \((\gamma=1.4)\) does 100 J of work when it is expanded isobarically. Then the heat given to the gas _________ J.

Asseretion \(A:\) If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is \(5\, {mm}\) and there are \(50\) total divisions on circular scale, then least count is \(0.001\, {cm}\). Reason \(R:\) Least Count \(=\frac{\text { Pitch }}{\text { Total divisions on circular scale }}\) In the light of the above statements, choose the most appropriate answer from the options given below:

The average energy released per fission for the nucleus of \({ }_{92}^{235} U\) is 190 MeV . When all the atoms of 47 g pure \({ }_{92}^{235} U\) undergo fission process, the energy released is \(\alpha \times 10^{23} MeV\). The value of \(\alpha\) is ___________.
(Avogadro Number \(=6 \times 10^{23}\) per mole)

One main scale division of a vernier caliper is equal to \(m\) units. If \(n^{\text {th }}\) division of main scale coincides with \((n+1)^{\mathrm{th}}\) division of vernier scale, the least count of the vernier caliper is _______.

A thin uniform rod of length \(2\,m\). cross sectional area ' \(A\) ' and density ' \(d\) ' is rotated about an axis passing through the centre and perpendicular to its length with angular velocity \(\omega\). If value of \(\omega\) in terms of its rotational kinetic energy \(E\) is \(\sqrt{\frac{\alpha E}{ Ad }}\) then the value of \(\alpha\) is \(...........\)

A concave mirror of focal length \(f\) in air is dipped in a liquid of refractive index \(\mu\). Its focal length in the liquid will be:

A transparent cube of side \(d\), made of a material of refractive index \(\mu_2\), is immersed in a liquid of refractive index \(\mu_1(\mu_1 < \mu_2)\). A ray is incident on the face \(AB\) at an angle \(\theta \) (shown in the figure). Total internal reflection takes place at point \(E\) on the face \(BC\). The \(\theta\) must satisfy

In the given figure, the block of mass \(m\) is dropped from the point ' \(A\) '. The expression for kinetic energy of block when it reaches point ' \(B\) ' is ................

A particle of mass \(m\) moves in a circular orbit in a central potential field \(U\left( r \right) = \frac{1}{2}k{r^2}\). If Bohr’s quantization conditions are applied, radii of possible orbits and energy levels vary with quantum number \(n\) as

The relation between time \(t\) and distance \(x\) for a moving body is given as \(t=m x^{2}+n x\), where \({m}\) and \({n}\) are constants. The retardation of the motion is - (Where \(v\) stands for velocity)

A square shaped coil of area \(70\,cm ^2\) having \(600\) turns rotates in a magnetic field of \(0.4\,wbm ^{-2}\), about an axis which is parallel to one of the side of the coil and perpendicular to the direction of field. If the coil completes \(500\) revolution in a minute, the instantaneous emf when the plane of the coil is inclined at \(60^{\circ}\) with the field, will be \(..........V\). (Take \(\pi=\frac{22}{7}\) )