The above \(P-V\) diagram represents the thermodynamic cycle of an engine, operating with an ideal monatomic gas. The amount of heat, extracted from the source in a single cycle is

The ratio of the coefficient of volume expansion of a glass container to that of a viscous liquid kept inside the container is \(1 : 4\). What fraction of the inner volume of the container should the liquid occupy so that the volume of the remaining vacant space will be same at all temperatures ?

The threshold frequency of metal is \(f_0\). When the light of frequency \(2 f_0\) is incident on the metal plate, the maximum velocity of photoelectron is \(v_1\). When the frequency of incident radiation is increased to \(5 f _0\). the maximum velocity of photoelectrons emitted is \(v_2\). The ratio of \(v_1\) to \(v_2\) is:

Consider a long thin conducting wire carrying a uniform current I. A particle having mass " M " and charge " \(q\) " is released at a distance " \(a\) " from the wire with a speed \(v_0\) along the direction of current in the wire. The particle gets attracted to the wire due to magnetic force. The particle turns round when it is at distance \(x\) from the wire. The value of \(x\) is [ \(\mu_0\) is vacuum permeability]

The distance \(x\) covered by a particle in one dimensional motion varies with time \(t\) as \(\mathrm{x}^{2}=\mathrm{at}^{2}+2 \mathrm{bt}+\mathrm{c.}\) If the acceleration of the particle depends on \(\mathrm{x}\) as \(\mathrm{x}^{-\mathrm{n}},\) where \(\mathrm{n}\) is an integer, the value of \(\mathrm{n}\) is

The average mass of rain drops is \(3.0\times10^{-5}\, kg\) and their avarage terminal velocity is \(9\, m/s\). Calculate the energy transferred by rain to each square metre of the surface at a place which receives \(100\, cm\) of rain in a year

Given below are two statements Statement \(I\) : The electric force changes the speed of the charged particle and hence changes its kinetic energy: whereas the magnetic force does not change the kinetic energy of the charged particle Statement \(II\) : The electric force accelerates the positively charged particle perpendicular to the direction of electric field. The magnetic force accelerates the moving charged particle along the direction of magnetic field. In the light of the above statements, choose the most appropriate answer from the options given below

For a transverse wave travelling along a straight line, the distance between two peaks (crests) is \(5 \,m ,\) while the distance between one crest and one trough is \(1.5 \,m\) The possible wavelengths (in \(m\) ) of the waves are

In an a.c. circuit, voltage and current are given by: \(V=100 \sin (100 t)\  V\) and \(I=100 \sin \left(100 t+\frac{\pi}{3}\right)\  \mathrm{mA}\) respectively. The average power dissipated in one cycle is _______.

The coercivity of a magnet is \(5 \times 10^3 \mathrm{~A} / \mathrm{m}\). The amount of current required to be passed in a solenord of length \(30 \mathrm{~cm}\) and the number of turns \(150\) , so that the magnet gets demagnetised when inside the solenoid is _______ A.

A gun mounted on the ground fires bullets in all directions with same speed. The farthest distance the bullets could reach is \(6.4\) m. The speed of the bullets from the gun is ______ m/s.
(take \(g=10\) m/s\(^2\))

A particle of mass \(m\) is moving along the \(x\) -axis with initial velocity \(u \hat i\). It collides elastically with a particle of mass \(10\, m\) at rest and then moves with half its initial kinetic energy (see figure). If \(\sin \theta_{1}=\sqrt{n} \sin \theta_{2}\) then value of \(n\) is.....