The elastic behaviour of material for linear streass and linear strain, is shown in the figure. The energy density for a linear strain of \(5 \times 10^{-4}\) is \(\dots \; kJ / m ^{3}\). Assume that material is elastic upto the linear strain of \(5 \times 10^{-4}\).

A convex lens (of focal length \(20\, cm\)) and a concave mirror, having their principal axes along the same lines, are kept \(80\, cm\) apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of \(30\, cm\) to the left of the convex lens, its image remains at the same position even if the concave mirror is removed. The maximum distance of the object for which this concave mirror, by itself would produce a virtual image would be.....\(cm\)

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 colour coding on a carbon resistor is shown in the given figure. The resistance value of the given resistor is:

A clock has a continuously moving second's hand of \(0.1\, m\) length. The average acceleration of the tip of the hand (in units of \(ms ^{-2}\) ) is of the order of

A series \(LCR\) circuit consists of \(R =80\,\Omega X _{ L }=100\, \Omega\) and \(X _{ C }=40\, \Omega\) The input voltage is \(2500 \cos (100 \pi t )\,V\). The amplitude of current, in the circuit, is \(................A.\)

Two plane mirrors are inclined to each other such that a ray of light incident to the first mirror \((M_1)\) and parallel to the second mirror \((M_2)\) is finally reflected from the second mirror \((M_2)\) parallel to the first mirror \((M_1).\) The angle between the two mirrors will be......\(^o\)

Assuming human pupil to have a radius of \(0.25\ cm\) and a comfortable viewing distance of \(25\ cm\), the minimum separation between two objects that human eye can resolve at \(500\ nm\) wavelength is.....\(\mu m\)

A particle undergoing simple harmonic motion has time dependent displacement given by \(x(t)\, = \,A\,\sin \,\frac{{\pi t}}{{90}}\). The ratio of kinetic to potential energy \(o\) the particle at \(t=210\,s\) will be

A uniform electric field \(\vec E\) exists between the plates of a charged condenser. A charged particle enters the space between the plates and perpendicular to \(\vec E\) . The path of the particle between the plates is a

Two cars \(P\) and \(Q\) are moving on a road in the same direction. Acceleration of car \(P\) increases linearly with time whereas car \(Q\) moves with a constant acceleration. Both cars cross each other at time \(t=0\), for the first time. The maximum possible number of crossing(s) (including the crossing at \(t=0)\) is ________.

In a double slit experiment, when a thin film of thickness \(t\) having refractive index \(\mu \) is introduced in front of one of the slits, the maximum at the centre of the fringe pattern shifts by one fringe width. The value of \(t\) is (\(\lambda \) is the wavelength of the light used)

Work done by a Carnot engine operating between temperatures \(127^{\circ}\,C\) and \(27^{\circ}\,C\) is \(2\,kJ\). The amount of heat transferred to the engine by the reservoir is \(........\,kJ\)