A diatomic gas \((\gamma=1.4)\) does \(100 \mathrm{~J}\) of work in an isobaric expansion. The heat given to the gas is _______.

An object of mass ' m ' is projected from origin in a vertical \(x y\) plane at an angle \(45^{\circ}\) with the x axis with an initial velocity \(\mathrm{v}_0\). The magnitude and direction of the angular momentum of the object with respect to origin, when it reaches at the maximum height, will be [ g is acceleration due to gravity]

As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion:

Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is \(16\). The intensity of the waves are in the ratio

The electric field due to a short electric dipole at a large distance (r) from center of dipole on the equatorial plane varies with distance as

An electromagnetic wave of frequency \(1\times10^{14}\, hertz\) is propagating along \(z-\) axis. The amplitude of electric field is \(4\, V/m\) . lf \({\varepsilon_0}=\, 8.8\times10^{-12}\, C^2/Nm^2\) , then average energy density of electric field will be:

Consider a badminton racket with length scales as shown in the figure.If the mass of the linear and circular portions of the badminton racket are same \((M)\) and the mass of the threads are negligible, the moment of inertia of the racket about an axis perpendicular to the handle and in the plane of the ring at, \(\frac{r}{2}\) distance from the end \(A\) of the handle will be ....... \(Mr^2\)?

Two projectiles are thrown with same initial velocity making an angle of \(45^{\circ}\) and \(30^{\circ}\) with the horizontal respectively. The ratio of their respective ranges will be.

Consider a block and trolley system as shown in figure. If the coefficient of kinetic friction between the trolley and the surface is \(0.04\) , the acceleration of the system in \(\mathrm{ms}^{-2}\) is _______. (Consider that the string is massless and unstretchable and the pulley is also massless and frictionless)

Velocity \((v)\) and acceleration \((a)\) in two systems of units \(1\) and \(2\) are related as \(V _{2}=\frac{ n }{ m ^{2}} v _{1}\) and \(a_{2}=\frac{a_{1}}{m n}\) respectively. Here \(m\) and \(n\) are constants. The relations for distance and time in two systems respectively are

The speed of a wave produced in water is given by \(v=\lambda^a g^b \rho^c\). Where \(\lambda\), g and \(\rho\) are wavelength of wave, acceleration due to gravity and density of water respectively. The values of \(a , b\) and \(c\) respectively, are