Nuclear Physics

Step 1: Given:
Step 2: The total power of an amplitude modulated (AM) wave is given by:
Step 3: Substitute the given values:
Step 4: Final Answer (up to two decimal places):

Step 1: Weight of the suspended mass: This is the tension in the vertical part of the rope.
Step 2: Let the tension in the inclined part of the rope be . Since the rope makes an angle of with the vertical and the system is in equilibrium, the vertical component of balances the weight:
Step 3:
Step 4: The horizontal force applied equals the horizontal component of the tension:
Step 5: Final Answer (up to two decimal places):

Step 1: Understand the physical situation. The radioactive nuclei are:
being produced at a constant rate ,
decaying simultaneously. After a long time, a steady state is reached where:
Step 2: Write the decay law. Let be the constant number of radioactive nuclei. Rate of decay: where is the decay constant.
Step 3: Express decay constant in terms of half-life.
Step 4: Apply steady-state condition. Substitute :
Hence, the constant number of radioactive nuclei is

Step 1: State the law of reflection. One of the fundamental laws of reflection states: Hence, option (A) is correct. Step 2: Apply trigonometric relation. If , then: So, option (B) is also correct. Step 3: Evaluate the ratio. From : which is a constant. Thus, option (C) is correct. Step 4: Final conclusion. Since statements (A), (B), and (C) are all correct, the correct answer is:

Step 1: Recall the ray diagram for a concave mirror. When an object is placed at infinity, the rays coming from it are parallel to the principal axis. Step 2: Formation of image. For a concave mirror, parallel rays converge at the principal focus after reflection. Step 3: Nature of the image formed. The image formed at the focus is:

Real
Inverted
Highly diminished (point-sized)
Step 4: Evaluate the options.

(A) Enlarged — incorrect
(B) Virtual — incorrect
(C) Erect — incorrect
(D) Real, inverted and diminished — correct ✔
Step 5: Final conclusion. The image formed is real, inverted and diminished.