A force of \(F=(5 y+20) \hat{j} \,N\) acts on a particle. The work done by this force when the particle is moved from \(y=0 \,m\) to \(y=10 \,{m}\) is \(...\,{J}.\)

A thin rod \(MN\), free to rotate in the vertical plane about the fixed end \(N\), is held horizontal . When the end \(M\) is released the speed of this end, when the rod makes an angle \(\alpha \) with the horizontal, will be proportional to ( see figure)

\(300 \,cal\). of heat is given to a heat engine and it rejects \(225 \,cal\). of heat. If source temperature is \(227^{\circ} C\), then the temperature of sink will be____\({ }^{\circ} C\).

A singly ionized magnesium atom \((A=24)\) ion is accelerated to kinetic energy \(5\,keV\) and is projected perpendicularly into a magnetic field \(B\) of the magnitude \(0.5\,T\). The radius of path formed will be___________ \(cm\)

Two simple harmonic waves having equal amplitudes of \(8\,cm\) and equal frequency of \(10\,Hz\) are moving along the same direction. The resultant amplitude is also \(8\,cm\). The phase difference between the individual waves is \(..................\) degree.

A wheel is rotaing freely with an angular speed \(\omega\) on a shaft. The moment of inertia of the wheel is \(I\) and the moment of inertia of the shaft is negligible. Another wheel of momet of inertia \(3I\) initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is :

If the earth suddenly shrinks to \(\frac{1}{64}\) th of its original volume with its mass remaining the same, the period of rotation of earth becomes \(\frac{24}{ x } h\). The value of \(x\) is \(.......\)

In a compound microscope, the magnified virtual image is formed at a distance of \(25\, cm\) from the eye-piece. The focal length of its objective lens is \(1\, cm .\) If the magnification is \(100\) and the tube length of the microscope is \(20\, cm ,\) then the focal length of the eye-piece lens (in \(cm\) ) is

The ratio of average electric energy density and total average energy density of electromagnetic wave is:

A straight wire carrying a current of \(14\,A\) is bent into a semicircular are of radius \(2.2\,cm\) as shown in the figure. The magnetic field produced by the current at the centre \((O)\) of the arc. is \(.........\,\times 10^{-4}\, T\)

Match List - I with List - II.

List-I	List-II
(A) Angular Impulse	(I) \(\left[M^0 L^2 T^{-2}\right]\)
(B) Latent Heat	(II) \(\left[M L^2 T^{-3} A^{-1}\right]\)
(C) Electrical resistivity	(III) \(\left[M L^2 T^{-1}\right]\)
(D) Electromotive force	(IV) \(\left[M L^3 T^{-3} A^{-2}\right]\)

A car \(P\) travelling at \(20\,ms ^{-1}\) sounds its horn at a frequency of \(400\,Hz\). Another car \(Q\) is travelling behind the first car in the same direction with a velocity \(40\,ms ^{-1}\). The frequency heard by the passenger of the car \(Q\) is approximately \(.......\,Hz\) [Take, velocity of sound \(=360\,ms ^{-1}\) ]