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Two metal wires of identical dimensions are connected in series. If $\sigma_1$ and $\sigma_2$ are the conductivities of the metal wires respectively, the effective conductivity of the combination is:
A metal wire has mass $(0.4 \pm 0.002)$ g, radius $(0.3 \pm 0.001)$ mm and length $(5 \pm 0.02)$ cm. The maximum possible percentage error in the measurement of density will nearly be
The net magnetic flux through any closed surface is
The efficiency of an ideal heat engine (Carnot heat engine) working between the freezing point and boiling point of water is:
A gas is compressed isothermally to half its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then:
If $Q$, $E$ and $W$ denote respectively the heat added, change in internal energy and the work done in a closed cyclic process, then
A thermodynamic system undergoes cyclic process ABCDA as shown in figure. The work done by the system in the cycle is:
The molar specific heats of an ideal gas at constant pressure and volume are denoted by $C_P$ and $C_V$, respectively. If $\gamma = \frac{C_P}{C_V}$ and $R$ is the universal gas constant, then $C_V$ is equal to:
The dimensional formula for impulse is:
One mole of an ideal gas goes from an initial state $A$ to the final state $B$ with two processes. It first undergoes isothermal expansion from volume $V$ to $3V$ and then its volume is reduced from $3V$ to $V$ at constant pressure. The correct $(P-V)$ diagram representing the two processes is:
During an isothermal expansion, a confined ideal gas does $-150\text{ J}$ of work against its surrounding. This implies that:
The internal energy change in a system that has absorbed $2 \text{ kcal}$ of heat and done $500 \text{ J}$ of work is:
In a double-slit experiment, the two slits are $1\text{ mm}$ apart and the screen is placed $1\text{ m}$ away. A monochromatic light of wavelength $500\text{ nm}$ is used. What will be the width of each slit for obtaining ten maxima of double-slit within the central maxima of a single-slit pattern?
An ideal gas undergoes a thermodynamic process described by the equation: $PV^2 = C$, where $C$ is a constant. The gas transitions from an initial state $(P_1, V_1, T_1)$ to a final state $(P_2, V_2, T_2)$. Which of the following statements is correct?
A gas undergoes an isothermal process. The specific heat capacity of the gas in the process is:
$4.0 \text{ g}$ of a gas occupies $22.4 \text{ L}$ at NTP. The specific heat capacity of the gas at constant volume is $5.0 \text{ J K}^{-1}\text{mol}^{-1}$. If the speed of sound in this gas at NTP is $952 \text{ ms}^{-1}$, then the heat capacity at constant pressure is: (Take gas constant $R = 8.3 \text{ J K}^{-1}\text{mol}^{-1}$)
A speed motorcyclist sees a traffic jam ahead of him. He slows down to $36 \text{ km/h}$. He finds that traffic has eased and a car moving in front of him at $18 \text{ km/h}$ is honking at a frequency of $1392 \text{ Hz}$. If the speed of sound is $343 \text{ m/s}$, the frequency of the honk as heard by him will be
A train moving at a speed of $220 \text{ ms}^{-1}$ towards a stationary object, emits a sound of frequency $1000 \text{ Hz}$. Some of the sound reaching the object gets reflected back to the train as an echo. The frequency of the echo as detected by the driver of the train is (speed of sound in air is $330 \text{ ms}^{-1}$)
A tuning fork of frequency $512 \text{ Hz}$ makes $4 \text{ beats/s}$ with the vibrating strings of a piano. The beat frequency decreases to $2 \text{ beats/s}$ when the tension in the piano strings is slightly increased. The frequency of the piano string before increasing the tension was:
Two points are located at a distance of $10 \text{ m}$ and $15 \text{ m}$ from the source of oscillation. The period of oscillation is $0.05 \text{ s}$ and the velocity of the wave is $300 \text{ m/s}$. What is the phase difference between the oscillations of two points?