AIPMT 2012 Mock Test

Two metallic spheres of radii $1\text{cm}$ and $3\text{cm}$ are given charges of $-1\times 10^{-2}\text{C}$ and $5\times 10^{-2}\text{C}$, respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is:

A proton carrying $1\text{MeV}$ kinetic energy is moving in a circular path of radius $R$ in uniform magnetic field. What should be the energy of an $\alpha$ -particle to describe a circle of same radius in the same field?

A circular platform is mounted on a frictionless vertical axle. Its radius $R=2\text{m}$ and its moment of inertia $I=200{\text{kg m}}^2$. It is initially at rest. A $50\text{kg}$ man stands on the edge and begins to walk along the edge at a speed of $1{\text{ms}}^{-1}$ relative to the ground. Time taken by the man to complete one revolution is:

The ratio of amplitude of magnetic field ($B_0$) to the amplitude of electric field ($E_0$) for an electromagnetic wave propagating in vacuum is equal to:

A magnetic needle suspended parallel to a magnetic field requires $\sqrt{3}\text{J}$ of work to turn it through $60^{\circ }$. The torque needed to maintain the needle in this position will be: