The period of oscillations of a magnet is 2 sec. When it is remagnetised so that the pole strength is 4 times its period will be

Options

A. 4 s
B. 1 s
C. 2 s
D. `(1)/(2) s`

Answer

To solve the problem step by step, we will use the formula for the period of oscillation of a magnet in a magnetic field.

### Step 1: Understand the formula for the period of oscillation
The period of oscillation \( T \) of a magnet is given by the formula:
\[ T = 2\pi \sqrt{\frac{I}{mB}} \]
where:
- \( I \) is the moment of inertia,
- \( m \) is the pole strength,
- \( B \) is the magnetic field strength.

### Step 2: Identify the initial conditions
From the problem, we know that:
- The initial period \( T_1 = 2 \) seconds.
- The initial pole strength is \( m \).

### Step 3: Determine the new pole strength after remagnetization
When the magnet is remagnetized, the pole strength becomes 4 times the original pole strength:
\[ m' = 4m \]

### Step 4: Substitute the new pole strength into the formula
The new period \( T_2 \) after remagnetization can be expressed as:
\[ T_2 = 2\pi \sqrt{\frac{I}{m'B}} = 2\pi \sqrt{\frac{I}{4mB}} \]

### Step 5: Simplify the expression for the new period
Using the property of square roots:
\[ T_2 = 2\pi \sqrt{\frac{I}{4mB}} = 2\pi \frac{1}{2} \sqrt{\frac{I}{mB}} = \frac{1}{2} T_1 \]
Substituting \( T_1 = 2 \) seconds:
\[ T_2 = \frac{1}{2} \times 2 = 1 \text{ second} \]

### Conclusion
The new period of oscillation after remagnetization is:
\[ \boxed{1 \text{ second}} \]