Statement-1 A charged particle when projected perpendiculary to a uniform magnetic field, its velocity is constant through out its motion
Statement-2 A charged particle its acceleration is zero
Statement-3 A charged particle when projected perpendicular to a uniform magnetic field, a magnetic force acts on it but that does not change particle's speed

Options

A. TTF
B. FFT
C. FFF
D. TFT

Answer

To analyze the statements regarding the motion of a charged particle in a uniform magnetic field, let's break down each statement step by step.

### Step 1: Analyze Statement 1
**Statement 1**: A charged particle when projected perpendicular to a uniform magnetic field, its velocity is constant throughout its motion.

- When a charged particle enters a magnetic field perpendicularly, it experiences a magnetic force that acts perpendicular to its velocity. This force causes the particle to move in a circular path.
- In circular motion, while the speed (magnitude of velocity) remains constant, the direction of the velocity changes continuously.
- Therefore, the velocity (which is a vector quantity) is not constant because its direction changes.

**Conclusion**: Statement 1 is **false**.

### Step 2: Analyze Statement 2
**Statement 2**: A charged particle, its acceleration is zero.

- The acceleration of a charged particle in a magnetic field is given by the formula \( a = \frac{F}{m} \), where \( F \) is the magnetic force.
- The magnetic force \( F \) on a charged particle moving in a magnetic field is given by \( F = qvB \sin(\theta) \). Here, \( \theta = 90^\circ \) when the particle is projected perpendicularly, which means \( \sin(90^\circ) = 1 \).
- Thus, the force is \( F = qvB \), which is not zero, leading to a non-zero acceleration.

**Conclusion**: Statement 2 is **false**.

### Step 3: Analyze Statement 3
**Statement 3**: A charged particle when projected perpendicular to a uniform magnetic field, a magnetic force acts on it but that does not change the particle's speed.

- As established, the charged particle experiences a magnetic force that causes it to move in a circular path.
- In uniform circular motion, the speed of the particle remains constant, even though the direction of the velocity changes due to the magnetic force acting perpendicular to the velocity.
- Therefore, while the particle’s direction changes, its speed (the magnitude of velocity) does not change.

**Conclusion**: Statement 3 is **true**.

### Final Conclusion
- Statement 1: **False**
- Statement 2: **False**
- Statement 3: **True**

Thus, the correct option is that Statement 3 is true while Statements 1 and 2 are false.

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