A charged particle is projected perpendicular to uniform magnetic field. It describes a circle, the quantities which are inversely proportional to specific charge are
i) Radius ii) K. E
iii) Time period iv) Momentum

Options

A. Only i&ii are true
B. Only i,ii&iv are true
C. Only ii & iii are true
D. Only i & iii are true

Answer

To solve the question, we need to analyze the relationship between the specific charge (charge per unit mass, \( \frac{q}{m} \)) of a charged particle and the quantities mentioned: radius (r), kinetic energy (K.E.), time period (T), and momentum (p) when the particle is moving in a magnetic field.

### Step-by-Step Solution:

1. **Understanding the Motion of the Charged Particle:**
When a charged particle moves perpendicular to a uniform magnetic field, it experiences a magnetic force that acts as a centripetal force, causing it to move in a circular path.

2. **Force Acting on the Particle:**
The magnetic force \( F \) acting on the particle is given by:
\[ F = qvB \]
where \( q \) is the charge, \( v \) is the velocity, and \( B \) is the magnetic field strength.

3. **Centripetal Force:**
The centripetal force required to keep the particle moving in a circle is given by:
\[ F = \frac{mv^2}{r} \]
where \( m \) is the mass of the particle and \( r \) is the radius of the circular path.

4. **Equating Forces:**
Setting the magnetic force equal to the centripetal force, we have:
\[ qvB = \frac{mv^2}{r} \]
Rearranging this gives:
\[ r = \frac{mv}{qB} \]
From this equation, we can see that the radius \( r \) is inversely proportional to the specific charge \( \frac{q}{m} \).

5. **Kinetic Energy:**
The kinetic energy \( K.E. \) of the particle is given by:
\[ K.E. = \frac{1}{2}mv^2 \]
From the earlier equation for radius, we can express \( v \) in terms of \( r \):
\[ v = \frac{qBr}{m} \]
Substituting this expression for \( v \) into the kinetic energy formula:
\[ K.E. = \frac{1}{2}m\left(\frac{qBr}{m}\right)^2 = \frac{1}{2}\frac{q^2B^2r^2}{m} \]
This shows that kinetic energy is directly proportional to the charge \( q \) and inversely proportional to the mass \( m \), thus not inversely proportional to the specific charge.

6. **Time Period:**
The time period \( T \) of the circular motion can be calculated as:
\[ T = \frac{2\pi r}{v} \]
Substituting \( r = \frac{mv}{qB} \):
\[ T = \frac{2\pi \left(\frac{mv}{qB}\right)}{v} = \frac{2\pi m}{qB} \]
This shows that the time period \( T \) is inversely proportional to the specific charge \( \frac{q}{m} \).

7. **Momentum:**
The momentum \( p \) of the particle is given by:
\[ p = mv \]
From the expression for \( v \):
\[ p = m\left(\frac{qBr}{m}\right) = qBr \]
This indicates that momentum is directly proportional to the charge \( q \), and thus not inversely proportional to the specific charge.

### Conclusion:
From the analysis, we conclude that:
- **Radius (r)** is inversely proportional to the specific charge.
- **Time Period (T)** is inversely proportional to the specific charge.
- **Kinetic Energy (K.E.)** is not inversely proportional to the specific charge.
- **Momentum (p)** is not inversely proportional to the specific charge.

Thus, the quantities that are inversely proportional to the specific charge are **Radius and Time Period**.

### Final Answer:
The correct options are:
- i) Radius
- iii) Time period