STATEMENT-1: When a machine gun fires n bullets per second each with kinetic energy k, power of the gun is P = nk
STATEMENT-2: Power P = work done/time.
STATEMENT-3: For uniform circular motion the instantaneous power delivered by centripetal force is always zero.

Options

A. T T T
B. F F F
C. T T F
D. F T T

Answer

To analyze the statements given in the question, let's break down each statement step by step:

### Step 1: Analyze Statement 1
**Statement**: When a machine gun fires n bullets per second each with kinetic energy k, power of the gun is P = nk.

**Explanation**:
- The power of a machine is defined as the rate at which work is done or energy is transferred.
- In this case, each bullet has a kinetic energy \( k \).
- If the machine gun fires \( n \) bullets in one second, the total energy transferred in that second is the kinetic energy of one bullet multiplied by the number of bullets:
\[ \text{Total Energy} = n \cdot k \]
- Therefore, the power \( P \) of the gun can be expressed as:
\[ P = \frac{\text{Total Energy}}{\text{Time}} = \frac{nk}{1} = nk \]
- Hence, Statement 1 is **True**.

### Step 2: Analyze Statement 2
**Statement**: Power P = work done/time.

**Explanation**:
- This is the fundamental definition of power in physics.
- Power is indeed defined as the amount of work done per unit time.
- Mathematically, it can be expressed as:
\[ P = \frac{W}{t} \]
where \( W \) is the work done and \( t \) is the time taken.
- Therefore, Statement 2 is also **True**.

### Step 3: Analyze Statement 3
**Statement**: For uniform circular motion, the instantaneous power delivered by centripetal force is always zero.

**Explanation**:
- In uniform circular motion, the centripetal force acts towards the center of the circular path.
- The displacement of the object in circular motion is tangential to the circle.
- The angle \( \theta \) between the direction of the centripetal force (radially inward) and the displacement (tangential) is \( 90^\circ \).
- The work done \( W \) by a force is given by:
\[ W = F \cdot d \cdot \cos(\theta) \]
- Since \( \theta = 90^\circ \), \( \cos(90^\circ) = 0 \), thus:
\[ W = F \cdot d \cdot 0 = 0 \]
- Consequently, the instantaneous power \( P \) which is the work done per unit time is also zero:
\[ P = \frac{W}{t} = \frac{0}{t} = 0 \]
- Therefore, Statement 3 is **True**.

### Conclusion
All three statements are true. The correct option is that all statements are true.