A hydrogen atom in is ground state absorbs \(10.2\;eV\) of energy. The angular momentum of electron of the hydrogen atom will increase by the value of ............... \(\times 10^{-34} \; J {s}\) (Given, Plank's constant \(\left.=6.6 \times 10^{-34} Js \right)\)

For an experimental expression \(y=\frac{32.3 \times 1125}{27.4}\), where all the digits are significant. Then to report the value of \(y\) we should write

Monochromatic light of frequency \(6 \times 10^{14} \mathrm{~Hz}\) is produced by a laser. The power emitted is \(2 \times 10^{-3} \mathrm{~W}\). How many photons per second on an average, are emitted by the source? (Given \(\mathrm{h}=6.63 \times 10^{-34} \mathrm{Js}\) )

A collimated beam of light of diameter 2 mm is propagating along x -axis. The beam is required to be expanded in a collimated beam of diameter 14 mm using a system of two convex lenses. If first lens has focal length 40 mm , then the focal length of second lens is _________ mm.

The position vector of a moving body at any instant of time is given as \(\vec{r}=\left(5 t^2 \hat{i}-5 t \hat{j}\right) \mathrm{m}\). The magnitude and direction of velocity at \(t=2 \mathrm{~s}\) is,

Two magnetic dipoles \(X\) and \(Y\) are placed at a separation \(d\), with their axes perpendicular to each other. The dipole moment of \(Y\) is twice that of \(X\). A particle of charge \(q\) is passing through their mid-point \(P\), at angle \(\theta  = 45^o\) with the horizontal line as shown in the figure. What would be the magnitude of force on the particle at that instant ? (\(d\) is much larger than the dimensions of the dipole)

The velocity-time graph of an object moving along a straight line is shown in figure. What is the distance covered by the object between \(t=0\) to \(t=4 \mathrm{~s}\) ?

Two planets \(A\) and \(B\) of equal mass are having their period of revolutions \(T_{A}\) and \(T_{B}\) such that \(T_{A}=2 T_{B}\). These planets are revolving in the circular orbits of radii \(I_{A}\) and \(I_{B}\) respectively. Which out of the following would be the correct relationship of their orbits?

A spherical ball of mass \(2\) kg falls from a height of \(10\) m and is brought to rest after penetrating \(10\) cm into sand. The average force exerted by sand on the ball is _______ N. (Take \(g = 10\) m/s\(^2\))

A block of mass \(1.9\, kg\) is at rest at the edge of a table, of height \(1\, m\). A bullet of mass \(0.1\, kg\) collides with the block and sticks to it. If the velocity of the bullet is \(20\, m / s\) in the horizontal direction just before the collision then the kinetic energy just before the combined system strikes the floor, is \(....J\) [Take \(g =10\, m / s ^{2}\). Assume there is no rotational motion and loss of energy after the collision is negligable. \(]\)

A long cylindrical volume contains a uniformly distributed charge of density \(\rho\). The radius of cylindrical volume is \(R\). A charge particle \((q)\) revolves around the cylinder in a circular path. The kinetic of the particle is