A particle moves along a horizontal circle witrr constant speed. If 'a' is its acceleration and 'E' is its kinetic energy
A) a is constant
B) E is constant
C) a is variable
D) E is variable

Options

A. a and b are correct
B. c and d are correct
C. a and d are correct
D. b and c are correct

Answer

To solve the problem, we need to analyze the motion of a particle moving in a horizontal circle with constant speed. Let's break down the concepts step-by-step.

### Step 1: Understanding Circular Motion
A particle moving in a horizontal circle with constant speed means that while the speed (magnitude of velocity) remains the same, the direction of the velocity vector is continuously changing.

**Hint:** Remember that speed is a scalar quantity, while velocity is a vector quantity that includes both magnitude and direction.

### Step 2: Analyzing Acceleration
In circular motion, the particle experiences centripetal acceleration directed towards the center of the circle. Although the magnitude of this centripetal acceleration can remain constant, the direction of the acceleration changes as the particle moves around the circle.

- Since the direction of the acceleration changes, we conclude that the acceleration is variable.

**Hint:** Consider how the direction of the acceleration vector changes even if its magnitude remains constant.

### Step 3: Analyzing Kinetic Energy
The kinetic energy (E) of the particle is given by the formula:
\[ E = \frac{1}{2} mv^2 \]
where:
- \( m \) is the mass of the particle (constant),
- \( v \) is the speed of the particle (constant).

Since both the mass and the speed are constant, the kinetic energy will also remain constant.

**Hint:** Kinetic energy depends on the square of the speed, so if the speed is constant, the kinetic energy must also be constant.

### Step 4: Conclusion
Based on our analysis:
- The acceleration \( a \) is variable (due to changing direction).
- The kinetic energy \( E \) is constant (since both mass and speed are constant).

Thus, the correct answers to the options given in the question are:
- A) a is constant: **False**
- B) E is constant: **True**
- C) a is variable: **True**
- D) E is variable: **False**

The correct options are B and C.

**Final Answer:** The correct options are B and C.