A: If a spring block system, oscillating in a vertical plane is made to oscillate on a horizontal surface, the time period will remain same.
R: The time period of spring block system does not depend on g.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2)
C. If Assertion is true statement but Reason is false then mark (3)
D. If both Assertion and Reason are false statements, then mark (4)

Answer

To analyze the statements given in the question, we need to evaluate both the Assertion (A) and the Reason (R) regarding the time period of a spring-block system.

### Step 1: Understanding the Time Period of a Spring-Block System
The time period (T) of a spring-block system is given by the formula:
\[ T = 2\pi \sqrt{\frac{m}{k}} \]
where:
- \( m \) is the mass of the block,
- \( k \) is the spring constant.

### Step 2: Analyzing the Assertion (A)
The assertion states that if a spring-block system oscillating in a vertical plane is made to oscillate on a horizontal surface, the time period will remain the same.

- When the system oscillates vertically, the gravitational force affects the equilibrium position of the spring but does not affect the time period of oscillation.
- When the system is moved to a horizontal surface, the gravitational force does not influence the oscillation since the spring's restoring force is still determined by the displacement from the equilibrium position.

Thus, the assertion (A) is **true**.

### Step 3: Analyzing the Reason (R)
The reason states that the time period of a spring-block system does not depend on \( g \) (acceleration due to gravity).

- From the formula for the time period, we can see that \( g \) does not appear in the equation.
- This indicates that the time period is independent of gravitational acceleration, confirming that the time period is solely dependent on mass and spring constant.

Thus, the reason (R) is also **true**.

### Step 4: Conclusion
Since both the assertion (A) and the reason (R) are true, and the reason correctly explains the assertion, we conclude that:
- The assertion is true, and the reason is true, and the reason is a correct explanation of the assertion.

### Final Answer:
Both A and R are true, and R is the correct explanation of A.

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