A source of sound S emitting waves of frequency 100 Hz and an observer O are located at some distance from each other. The source is moving with a speed of 19.4 ms-1 at an angle of with the source-observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer (velocity of sound in air 330 ms-1), is:
1. 100 Hz
2. 103 Hz
3. 106 Hz
4. 97 Hz
If dimensions of critical velocity \({v_c}\) of a liquid flowing through a tube are expressed as \(\eta^{x}\rho^yr^{z}\), where \(\eta, \rho~\text{and}~r\) are the coefficient of viscosity of the liquid, the density of the liquid, and the radius of the tube respectively, then the values of \({x},\) \({y},\) and \({z},\) respectively, will be:
1. \(1,-1,-1\)
2. \(-1,-1,1\)
3. \(-1,-1,-1\)
4. \(1,1,1\)
\(4.0~\text{gm}\) of gas occupies \(22.4~\text{litres}\) at NTP. The specific heat capacity of the gas at a constant volume is \(5.0~\text{JK}^{-1}\text{mol}^{-1}.\) If the speed of sound in the gas at NTP is \(952~\text{ms}^{-1},\) then the molar heat capacity at constant pressure will be:
(\(R=8.31~\text{JK}^{-1}\text{mol}^{-1}\))
1. | \(8.0~\text{JK}^{-1}\text{mol}^{-1}\) | 2. | \(7.5~\text{JK}^{-1}\text{mol}^{-1}\) |
3. | \(7.0~\text{JK}^{-1}\text{mol}^{-1}\) | 4. | \(8.5~\text{JK}^{-1}\text{mol}^{-1}\) |
If vectors \(\overrightarrow{{A}}=\cos \omega t \hat{{i}}+\sin \omega t \hat{j}\) and \(\overrightarrow{{B}}=\cos \left(\frac{\omega t}{2}\right)\hat{{i}}+\sin \left(\frac{\omega t}{2}\right) \hat{j}\) are functions of time. Then, at what value of \(t\) are they orthogonal to one another?
1. \(t = \frac{\pi}{4\omega}\)
2. \(t = \frac{\pi}{2\omega}\)
3. \(t = \frac{\pi}{\omega}\)
4. \(t = 0\)
In the given figure, a diode \(D\) is connected to an external resistance \(R = 100~\Omega\) and an EMF of \(3.5~\text{V}\). If the barrier potential developed across the diode is \(0.5~\text{V}\), the current in the circuit will be:
1. \(30~\text{mA}\)
2. \(40~\text{mA}\)
3. \(20~\text{mA}\)
4. \(35~\text{mA}\)
If potential \([\text{in volts}]\) in a region is expressed as \(V[x,y,z] = 6xy-y+2yz,\) the electric field \([\text{in N/C}]\) at point \((1, 1, 0)\) is:
1. | \(- \left(3 \hat{i} + 5 \hat{j} + 3 \hat{k}\right)\) | 2. | \(- \left(6 \hat{i} + 5 \hat{j} + 2 \hat{k}\right)\) |
3. | \(- \left(2 \hat{i} + 3 \hat{j} + \hat{k}\right)\) | 4. | \(- \left(6 \hat{i} + 9 \hat{j} + \hat{k}\right)\) |
A remote sensing satellite of earth revolves in a circular orbit at a height of \(0.25 \times10^6~\text{m}\) above the surface of the earth. If Earth’s radius is \(6.38\times10^6~\text{m}\) and \(g=9.8~\text{ms}^{-2}\), then the orbital speed of the satellite is:
1. \(7.76~\text{kms}^{-1}\)
2. \(8.56~\text{kms}^{-1}\)
3. \(9.13~\text{kms}^{-1}\)
4. \(6.67~\text{kms}^{-1}\)
Two metal wires of identical dimensions are connected in series. If \(\sigma_1\)
1. | \(\frac{2\sigma_1 \sigma_2}{\sigma_1+\sigma_2}\) | 2. | \(\frac{\sigma_1 +\sigma_2}{2\sigma_1\sigma_2}\) |
3. | \(\frac{\sigma_1 +\sigma_2}{\sigma_1\sigma_2}\) | 4. | \(\frac{\sigma_1 \sigma_2}{\sigma_1+\sigma_2}\) |
A satellite S is moving in an elliptical orbit around the earth. If the mass of the satellite is very small as compared to the mass of the earth, then:
1. | The angular momentum of S about the centre of the earth changes in direction, but its magnitude remains constant. |
2. | The total mechanical energy of S varies periodically with time. |
3. | The linear momentum of S remains constant in magnitude. |
4. | The acceleration of S is always directed towards the centre of the earth. |
Two particles \(\mathrm{A}\) and \(\mathrm{B}\), move with constant velocities \(\overrightarrow{{v}_1}\) and \(\overrightarrow{{v}_2}\) respectively. At the initial moment, their position vectors are \(\overrightarrow{{r}_1}\) and \(\overrightarrow{{r}_2}\) respectively. The condition for particles \(\mathrm{A}\) and \(\mathrm{B}\) for their collision will be:
1.\(\dfrac{\vec{r_1}-\vec{r_2}}{\left|\vec{r_1}-\vec{r_2}\right|}=\dfrac{\vec{v_2}-\vec{v_1}}{\left|\vec{v_2}-\vec{v_1}\right|}\)
2. \(\vec{r_1} \cdot \vec{v_1}=\vec{r_2} \cdot \vec{v_2}\)
3. \(\vec{r_1} \times \vec{v_1}=\vec{r_2} \times \vec{v_2}\)
4. \(\vec{r_1}-\vec{r_2}=\vec{v_1}-\vec{v_2}\)