AIEEE 2010 PYQ Mock Test

A rectangular loop has a sliding connector $\text{PQ}$ of length $l$ and resistance $R\Omega$ and it is moving with a speed $v$ as shown. The set-up is placed in a uniform magnetic field $B$ going into the plane of the paper. The three currents $I_1,I_2$ and $I$ (where $I$ is through the connector) are:

Let $C$ be the capacitance of a capacitor discharging through a resistor $R$. Suppose $t_1$ is the time taken for the energy stored in the capacitor to reduce to half its initial value and $t_2$ is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio $t_1/t_2$ will be:

Statement-1: Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.Statement-2: Principle of conservation of momentum holds true for all kinds of collisions.

Statement-1: When ultraviolet light is incident on a photocell, its stopping potential is $V_0$ and the maximum kinetic energy of the photoelectrons is $K_{max}$. When the ultraviolet light is replaced by X-rays, both $V_0$ and $K_{max}$ increase.Statement-2: Photoelectrons are emitted with speeds ranging from zero to a maximum value because of the range of frequencies present in the incident light.

A ball is made of a material of density $\rho$ where ${\rho }_{oil}<\rho <{\rho }_{water}$ with ${\rho }_{oil}$ and ${\rho }_{water}$ representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following describes its equilibrium position?