Question Bank Directory

The terminal velocity of a copper ball of radius $5 \text{ mm}$ falling through a tank of oil at room temperature is $10 \text{ cm s}^{-1}$. If the viscosity of oil at room temperature is $0.9 \text{ kg m}^{-1} \text{ s}^{-1}$, the viscous drag force is:

The bulk modulus of a spherical object is $B$. If it is subjected to uniform pressure $P$, the fractional decrease in radius will be:

The following figures show the arrangement of bar magnets in different configurations. Each magnet has a magnetic dipole moment $\mathbf{m}$. Which configuration has the highest net magnetic dipole moment?

A compass needle which is allowed to move in a horizontal plane is taken to a geomagnetic pole. It:

Two small spherical metal balls, having equal masses, are made from materials of densities $\rho_1$ and $\rho_2$ such that $\rho_1 = 8\rho_2$ and having radii of $1 \text{ mm}$ and $2 \text{ mm}$, respectively. They are made to fall vertically (from rest) in a viscous medium whose coefficient of viscosity equals $\eta$ and whose density is $0.1\rho_2$. The ratio of their terminal velocities would be:

A convex lens and a concave lens, each having the same focal length of $25\text{ cm}$, are put in contact to form a combination of lenses. The power in dioptres of the combination is:

Select the correct option based on the statements: Statement I: The magnetic field of a circular loop at very far away point on the axial line varies with distance as like that of a magnetic dipole. Statement II: The magnetic field due to magnetic dipole varies inversely with the square of the distance from the centre on the axial line.

A soap bubble, having radius of $1\text{ mm}$, is blown from a detergent solution having a surface tension of $2.5 \times 10^{-2}\text{ N/m}$. The pressure inside the bubble equals at a point $Z_0$ below the free surface of water in a container. Taking $g = 10\text{ m/s}^2$, density of water $= 10^3\text{ kg/m}^3$, the value of $Z_0$ is :

A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass same. Which of the following physical quantities would remain constant for the sphere?

The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is:

Two racing cars of masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$ respectively. Their speeds are such that each makes a complete circle in the same duration of time $t$. The ratio of the angular speed of the first to the second car is:

Match List-I with List-II. **List-I (Material)** (A) Diamagnetic (B) Ferromagnetic (C) Paramagnetic (D) Non-magnetic **List-II (Susceptibility $\chi$)** (I) $\chi = 0$ (II) $0 > \chi \ge -1$ (III) $\chi \gg 1$ (IV) $0 < \chi < \epsilon$ (a small positive number) Choose the correct answer from the options given below:

A wire of length $L$, area of cross section $A$ is hanging from a fixed support. The length of the wire changes to $L_1$ when mass $M$ is suspended from its free end. The expression for Young's modulus is:

Two wires are made of the same material and have the same volume. The first wire has a cross-sectional area $A$ and the second wire has a cross-sectional area $3A$. If the length of the first wire is increased by $\Delta l$ on applying a force $F$, how much force is needed to stretch the second wire by the same amount?

A 150 m long train is moving to north at a speed of 10 m/s. A parrot flying towards south with a speed of 5 m/s crosses the train. The time taken by the parrot to cross the train would be:

The angular speed of the seconds needle in a mechanical watch is:

In a uniform magnetic field of $0.049 \text{ T}$, a magnetic needle performs $20$ complete oscillations in $5$ seconds as shown. The moment of inertia of the needle is $9.8 \times 10^{-6} \text{ kg m}^2$. If the magnitude of magnetic moment of the needle is $x \times 10^{-5} \text{ Am}^2$, then the value of '$x$' is:

A stone tied to the end of a string of 1 m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolutions in 44 s, what is the magnitude and direction of acceleration of the stone?

Let a wire be suspended from the ceiling (rigid support) and stretched by a weight $W$ attached at its free end. The longitudinal stress at any point of the cross-sectional area $A$ of the wire is:

Given below are two statements: Statement I: $Cr^{2+}$ is oxidising agent and $Mn^{3+}$ is a reducing agent in nature. Statement II: $Sc^{3+}$ compounds are repelled by the applied magnetic field. In light of the above statements, choose the most appropriate answer from the options given below: