The approximate depth of an ocean is \(2700~\text{m}\). The compressibility of water is \(45.4\times10^{-11}~\text{Pa}^{-1}\) and the density of water is \(10^{3}~\text{kg/m}^3\). What fractional compression of water will be obtained at the bottom of the ocean?
| 1. | \(0.8\times 10^{-2}\) | 2. | \(1.0\times 10^{-2}\) |
| 3. | \(1.2\times 10^{-2}\) | 4. | \(1.4\times 10^{-2}\) |
The two ends of a metal rod are maintained at temperatures \(100~^\circ\text{C}\) and \(110~^\circ\text{C}.\) The rate of heat flow in the rod is found to be \(4.0\) J/s. If the ends are maintained at temperatures \(200~^\circ \text{C}\) and \(210 ~^\circ \text{C},\) the rate of heat flow will be:
| 1. | \(44.0\) J/s | 2. | \(16.8\) J/s |
| 3. | \(8.0\) J/s | 4. | \(4.0\) J/s |
\((\rho_{\text {air }}=1.2~\text{kg/m}^3)\)
| 1. | \(4 \times 10^5~\text N,\) downwards | 2. | \(4 \times 10^5~\text N,\) upwards |
| 3. | \(2.4 \times 10^5~\text N,\) upwards | 4. | \(2.4 \times 10^5~\text N,\) downwards |
The figure below shows two paths that may be taken by gas to go from state \(A\) to state \(C.\)
In process \(AB,\) \(400~\text{J}\) of heat is added to the system, and in process \(BC,\) \(100~\text{J}\) of heat is added to the system. The heat absorbed by the system in the process \(AC\) will be:
1. \(380~\text{J}\)
2. \(500~\text{J}\)
3. \(460~\text{J}\)
4. \(300~\text{J}\)
A Carnot engine, having an efficiency of = as a heat engine, is used as a refrigerator. If the work done on the system is \(10\) J, the amount of energy absorbed from the reservoir at a lower temperature is:
1. \(100\) J
2. \(99\) J
3. \(90\) J
4. \(1\) J
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:
| 1. | \(20~\text{kJ}\) | 2. | \(-20~\text{kJ}\) |
| 3. | \(20~\text{J}\) | 4. | \(-12~\text{kJ}\) |
| 1. | \(\left(1+\frac{1}{n}\right )\) | 2. | \(\left(1+\frac{n}{3}\right)\) |
| 3. | \(\left(1+\frac{2}{n}\right)\) | 4. | \(\left(1+\frac{n}{2}\right)\) |
When two displacements are represented by \(y_1 = a \text{sin}(\omega t)\) and \(y_2 = b\text{cos}(\omega t)\) are superimposed, then the motion is:
| 1. | not simple harmonic. |
| 2. | simple harmonic with amplitude \(\dfrac{a}{b}\). |
| 3. | simple harmonic with amplitude \(\sqrt{a^2+b^{2}}.\) |
| 4. | simple harmonic with amplitude \(\dfrac{a+b}{2}\). |
A particle is executing SHM along a straight line. Its velocities at distances \(x_1\) and \(x_2\) from the mean position are \(v_1\) and \(v_2\), respectively. Its time period is:
| 1. | \(2 \pi \sqrt{\dfrac{x_{1}^{2}+x_{2}^{2}}{v_{1}^{2}+v_{2}^{2}}}~\) | 2. | \(2 \pi \sqrt{\dfrac{{x}_{2}^{2}-{x}_{1}^{2}}{{v}_{1}^{2}-{v}_{2}^{2}}}\) |
| 3. | \(2 \pi \sqrt{\dfrac{v_{1}^{2}+v_{2}^{2}}{x_{1}^{2}+x_{2}^{2}}}\) | 4. | \(2 \pi \sqrt{\dfrac{v_{1}^{2}-v_{2}^{2}}{x_{1}^{2}-x_{2}^{2}}}\) |
The fundamental frequency of a closed organ pipe of a length \(20\) cm is equal to the second overtone of an organ pipe open at both ends. The length of the organ pipe open at both ends will be:
| 1. | \(80\) cm | 2. | \(100\) cm |
| 3. | \(120\) cm | 4. | \(140\) cm |
© 2026 GoodEd Technologies Pvt. Ltd.