A gas mixture consists of \(3\) moles of oxygen and \(5\) moles of argon at temperature \(T\). Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of \(RT\) ) of the mixture is

In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of \(\mathrm{M}^{\mathrm{P}} \mathrm{L}^{\mathrm{Q}} \mathrm{T}^{\mathrm{R}} \mathrm{A}^{\mathrm{S}}\), where value of ' Q ' and ' R ' are

If \(\mathrm{G}\) be the gravitational constant and \(\mathrm{u}\) be the energy density then which of the following quantity have the dimension as that the \(\sqrt{\mathrm{uG}}\)?

The position vector of the centre of mass \(\vec r\, cm\) of an asymmetric uniform bar of negligible area of cross-section as shown in figure is

The strain-stress plot for materials A, B, C and D is shown in the figure. Which material has the largest Young's modulus?

The trajectory of a projectile in a vertical plane is \(y =\alpha x -\beta x ^{2},\) where \(\alpha\) and \(\beta\) are constants and \(x \& y\) are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection \(\theta\) and the maximum height attained \(H\) are respectively given by :-

Assuming the earth to be a sphere of uniform mass density, a body weighed \(300 \mathrm{~N}\) on the surface of earth. How much it would weigh at \(R / 4\) depth under surface of earth?

A \(12.5\, eV\) electron beam is used to bombard gaseous hydrogen at room temperature. It will emit

In a linear simple harmonic motion \((SHM)\) \((A)\) Restoring force is directly proportional to the displacement. \((B)\) The acceleration and displacement are opposite in direction. \((C)\) The velocity is maximum at mean position. \((D)\) The acceleration is minimum at extreme points. Choose the correct answer from the options given below :

A stone tide to a string of length \(L\) is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed \(u\). The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is \(\sqrt{ x \left( u ^{2}- gL \right)}\). The value of \(x\) is .............

The general displacement of a simple harmonic oscillator is \(x = A \sin \omega t\). Let \(T\) be its time period. The slope of its potential energy (U) - time (t) curve will be maximum when \(t=\frac{T}{\beta}\). The value of \(\beta\) is \(.........\)

A spherical liquid drop of radius \(R\) acquires the terminal velocity \(v_1\) when falls through a gas of viscosity \(\eta\). Now the drop is broken into \(64\) identical droplets and each droplet acquires terminal velocity \(v_2\) falling through the same gas. The ratio of terminal velocities \(v_1/v_2\) is ________.