Fluids

Step 1: Formula for potential energy in a simple pendulum.
The potential energy at the extreme position (where the amplitude is ) is given by: where is the height raised by the pendulum. For small oscillations, , where is the angle corresponding to the extreme position.
Step 2: Using the amplitude.
For maximum displacement , the potential energy becomes:
Step 3: Conclusion.
Thus, the correct answer is (A) .

Step 1: Understanding the problem.
The difference in heights of the liquid at the centre and at the edge of a rotating liquid surface can be derived using the concept of centrifugal force acting on the liquid. The pressure difference in the liquid due to this force results in a height difference.
Step 2: Using the equation for height difference.
The height difference can be related to the centrifugal force by the formula: where is the radius of the vessel, is the angular velocity, and is the acceleration due to gravity.
Step 3: Conclusion.
Thus, the correct answer is (D) .

Concept:
For transistor: Step 1: Given value.
Step 2: Calculate .
Step 3: Conclusion. Current gain =

Step 1: Fundamental Mode
Closed pipe: Fundamental mode has 1 Node (at closed end) and 1 Antinode (at open end).
Step 2: Overtones
- 1st Overtone (3rd Harmonic): 2 Nodes, 2 Antinodes.
- 2nd Overtone (5th Harmonic): 3 Nodes, 3 Antinodes.
Step 3: Conclusion
In the second overtone of a closed pipe, there are 3 nodes and 3 antinodes.
Final Answer: (A)