AIPMT 2009 Preliminary Mock Test

Three concentric spherical shells have radii $a,b$ and $c$ ($a<b<c$) and have surface charge densities $\sigma ,-\sigma$ and $\sigma$ respectively. If $V_A,V_B$ and $V_C$ denote the potentials of the three shells, then for $c=a+b$, we have:

An engine pumps water continuously through a hose. Water leaves the hose with a velocity $v$ and $m$ is the mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water?

A bar magnet having a magnetic moment of $2\times 10^4{\text{JT}}^{-1}$ is free to rotate in a horizontal plane. A horizontal magnetic field $B=6\times 10^{-4}\text{T}$ exists in the space. The work done in taking the magnet slowly from a direction parallel to the field to a direction $60^{\circ }$ from the field is:

In a Rutherford scattering experiment when a projectile of charge $z_1$ and mass $M_1$ approaches a target nucleus of charge $z_2$ and mass $M_2$, the distance of closest approach is $r_0$. The energy of the projectile is:

Monochromatic light of wavelength $667\text{nm}$ is produced by a helium neon laser. The power emitted is $9\text{mW}$. The number of photons arriving per sec. on the average at a target irradiated by this beam is: