Assertion : If a pendulum is suspended in a lift and lift accelerates upwards, then its time period will decrease.
Reason : Effective value of g will be
`g_(e)=g+a`

Options

A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Explanation

To solve the question, we need to analyze the assertion and the reason provided regarding the behavior of a pendulum in an accelerating lift.

### Step-by-Step Solution:

1. **Understanding the Pendulum's Time Period**:
The time period \( T \) of a simple pendulum is given by the formula:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where \( L \) is the length of the pendulum and \( g \) is the acceleration due to gravity.

2. **Effect of Lift's Acceleration**:
When the lift accelerates upwards with an acceleration \( a \), the effective acceleration due to gravity \( g_e \) experienced by the pendulum bob changes. The effective gravitational acceleration can be expressed as:
\[ g_e = g + a \]
This is because the upward acceleration of the lift adds to the gravitational pull acting on the pendulum bob.

3. **Substituting Effective Gravity into the Time Period Formula**:
Substituting \( g_e \) into the time period formula, we get:
\[ T = 2\pi \sqrt{\frac{L}{g + a}} \]
Since \( g + a \) is greater than \( g \), the denominator of the fraction increases.

4. **Analyzing the Impact on Time Period**:
As the denominator \( g + a \) increases, the overall value of \( T \) (the time period) decreases. Therefore, when the lift accelerates upwards, the time period of the pendulum decreases.

5. **Conclusion**:
The assertion states that if a pendulum is suspended in a lift that accelerates upwards, then its time period will decrease. This is true. The reason provided states that the effective value of \( g \) will be \( g_e = g + a \), which is also true. Thus, both the assertion and reason are correct.

### Final Answer:
Both the assertion and reason are true.