AIEEE 2006 Mock Test

Four point masses, each of value $m$, are placed at the corners of a square $ABCD$ of side $\ell$. The moment of inertia through $A$ and parallel to $BD$ is:

A wire elongates by $\ell \text{mm}$ when a load $W$ is hanged from it. If the wire goes over a pulley and two weights $W$ each are hung at the two ends, the elongation of the wire will be (in mm):

Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature $T_0$, while Box B contains one mole of helium at temperature $(7/3)T_0$. The boxes are put into thermal contact. The final temperature $T_f$ is:

Two spherical conductors $A$ and $B$ of radii $1\text{mm}$ and $2\text{mm}$ are separated by a distance of $5\text{cm}$ and are uniformly charged. If the spheres are connected by a conducting wire, then in equilibrium, the ratio of the magnitude of the electric fields at the surface of spheres $A$ and $B$ is:

An inductor ($L=100\text{mH}$), a resistor ($R=100\Omega$) and a battery ($E=100\text{V}$) are connected in series. After a long time, the battery is disconnected after short-circuiting. The current in the circuit $1\text{ms}$ after the short-circuit is: