AIEEE 2008 PYQ Mock Test

Electrons accelerated by potential $V$ are diffracted from a crystal. If $d=1\text{A˚}$ and $i=30^{\circ }$, $V$ should be about ($h=6.6\times 10^{-34}\text{J s},m_e=9.1\times 10^{-31}\text{kg},e=1.6\times 10^{-19}\text{C}$):

If a strong diffraction peak is observed when electrons are incident at an angle ‘$i$ ’ from the normal to the crystal planes with distance ‘$d$ ’ between them, de Broglie wavelength ${\lambda }_{dB}$ of electrons can be calculated by the relationship ($n$ is an integer):

In an experiment, electrons pass through a narrow slit of width ‘$d$ ’. They are detected on a screen at a distance ‘$D$ ’. Which graph correctly represents the number of electrons $N$ detected as a function of the detector position $y$ ($y=0$ corresponds to the middle of the slit)?

A planet in a distant solar system is $10$ times more massive than the earth and its radius is $10$ times smaller. Given that the escape velocity from the earth is $11\text{km/s}$, the escape velocity from the surface of the planet would be:

A spherical solid ball of volume $V$ is made of a material of density ${\rho }_1$. It is falling through a liquid of density ${\rho }_2$ (${\rho }_2<{\rho }_1$). Assume that the liquid applies a viscous force $F_{\text{viscous}}=-k{v}^2$. The terminal speed of the ball is: