Question Bank Directory

In the diagram shown, the normal reaction force between $2 \text{ kg}$ and $1 \text{ kg}$ blocks is: (Consider the surface to be smooth and $g=10 \text{ m/s}^2$)

Given below are two statements: Assertion (A): A standing bus suddenly accelerates. If there was no friction between the feet of a passenger and the floor of the bus, the passenger would move back. Reason (R): In the absence of friction, the floor of the bus would slip forward under the feet of the passenger.

A slab of stone of area of $0.36\text{ m}^2$ and thickness $0.1\text{ m}$ is exposed on the lower surface to steam at $100^{\circ}\text{C}$. A block of ice at $0^{\circ}\text{C}$ rests on the upper surface of the slab. In one hour $4.8\text{ kg}$ of ice is melted. The thermal conductivity of slab is : (Given latent heat of fusion of ice $=3.36 \times 10^5\text{ J kg}^{-1}$)

One mole of an ideal diatomic gas undergoes a transition from $A$ to $B$ along a path $AB$ as shown in the figure. The change in internal energy of the gas during the transition is

A point mass $m$ is moved in a vertical circle of radius $r$ with the help of a string. The velocity of the mass is $\sqrt{7gr}$ at the lowest point. The tension in the string at the lowest point is:

A ball of mass 0.15 kg is dropped from a height 10 m, strikes the ground, and rebounds to the same height. The magnitude of impulse imparted to the ball is ($g=10 \text{ m/s}^2$) nearly:

Liquid oxygen at $50\text{ K}$ is heated to $300\text{ K}$ at constant pressure of $1\text{ atm}$. The rate of heating is constant. Which one of the following graphs represents the variation of temperature with time?

A refrigerator works between $4^{\circ}\text{C}$ and $30^{\circ}\text{C}$. It is required to remove $600 \text{ calories}$ of heat every second to keep the temperature of the refrigerated space constant. The power required will be: (Take, $1 \text{ cal} = 4.2 \text{ Joules}$)

For an adiabatic process, the factor which remains constant is: (all the notations have their usual meaning)

When a string is divided into three segments of lengths $l_1, l_2$ and $l_3$, the fundamental frequencies of these three segments are $\nu_1, \nu_2$ and $\nu_3$ respectively. The original fundamental frequency ($\nu$) of the string is:

In which of the following molecules are all the bonds not equal?

A metallic bar of Young's modulus $0.5 \times 10^{11}\text{ N m}^{-2}$, coefficient of linear thermal expansion $10^{-5}\ ^\circ\text{C}^{-1}$, length $1\text{ m}$ and cross-sectional area $10^{-3}\text{ m}^2$ is heated from $0^\circ\text{C}$ to $100^\circ\text{C}$ without expansion or bending. The compressive force developed in the metallic bar is:

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of $C_P/C_V$ for the gas is equal to:

The potential difference across the 100 Ω resistance in the following circuit is measured by a voltmeter of 900 Ω resistance. The percentage error made in reading the potential difference is:

Zr ($Z = 40$) and Hf ($Z = 72$) have similar atomic and ionic radii because of :

The measurement of an unknown resistance R is to be carried out using a Wheatstone bridge. Two students perform an experiment in two ways. The first student takes R₂ = 10 Ω and R₁ = 5 Ω. The other student takes R₂ = 1000 Ω and R₁ = 500 Ω. In the standard arm, both take R₃ = 5 Ω. Both find R = (R₂/R₁) × R₃ = 10 Ω within errors. Consider the following statements: (a) The errors of measurement of the two students are the same. (b) Errors of measurement do depend on the accuracy with which R₂ and R₁ can be measured. (c) If the student uses large values of R₂ and R₁, the currents through the arms will be feeble. This will make the determination of the null point accurately more difficult. (d) Wheatstone Bridge is a very accurate instrument and has no errors of measurement. Choose the correct option from the given ones:

Two rods, one made of copper and the other made of steel, of the same length and same cross-sectional area are joined together. The thermal conductivity of copper and steel are $385\text{ J s}^{-1}\text{K}^{-1}\text{m}^{-1}$ and $50\text{ J s}^{-1}\text{K}^{-1}\text{m}^{-1}$ respectively. The free ends of copper and steel are held at $100^{\circ}\text{C}$ and $0^{\circ}\text{C}$ respectively. The temperature at the junction is, nearly:

The equivalent capacitance of the combination shown in the figure is

Two equal negative charges of charge -q are fixed at the points (0, a) and (0, -a) on the Y-axis. A positive charge Q is released from rest at the point (2a, 0) on the X-axis. The charge Q will:

If the nuclear radius of ${}^{27}\mathrm{Al}$ is 3.6 Fermi, the approximate nuclear radius of ${}^{64}\mathrm{Cu}$ in Fermi is: