A material has Poisson's ratio \(0.50.\) If a uniform rod of it suffers a longitudinal strain of \(2 \times {10^{ - 3}}\), then the percentage change in volume is

Given below are two statements : Statement \(I\) : When the white light passed through a prism, the red light bends lesser than yellow and violet. Statement \(II\) : The refractive indices are different for different wavelengths in dispersive medium.
In the light of the above statements, choose the correct answer from the options given below :

Light from a point source in air falls on a convex curved surface of radius \(20 \mathrm{~cm}\) and refractive index \(1.5.\) If the source is located at \(100 \mathrm{~cm}\) from the convex surface, the image will be formed at _______ \(\mathrm{cm}\) from the object.

An effective power of a combination of \(5\) identical convex lenses which are kept in contact along the principal axis is \(25 \mathrm{D}\). Focal length of each of the convex lens is _______.

Two identical particles each of mass \(m\) go round a circle of radius \(a\) under the action of their mutual gravitational attraction. The angular speed of each particle will be

At which temperature the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at \(47^{\circ} \mathrm{C}\) ?

A particle is moving in a circular path of radius \(a,\) with a constant velocity \(v\) as shown in the figure.The centre of circle is marked by \('C'\). The angular momentum from the origin \(O\) can be written as

A cyclist starts from the point \(P\) of a circular ground of radius \(2 \mathrm{~km}\) and travels along its circumference to the point \(\mathrm{S}\). The displacement of a cyclist is _______.

The centre of a wheel rolling on a plane surface moves with a speed \(v_{0} .\) A particle on the rim of the wheel at the same level as the centre will be moving at a speed \(\sqrt{x}\, v_{0}\). Then the value of \(x\) is ...... .

An electron rotates in a circle around a nucleus having positive charge \(\mathrm{Ze}\). Correct relation between total energy ( \(E\) ) of electron to its potential energy \((U)\) is _______.