The correct answer is Option 3: The length of the pendulum increases.

The Physics Behind It

The time it takes for a pendulum to complete one full back-and-forth swing is called its time period ($T$). This is calculated using the standard pendulum formula:

$$T = 2\pi \sqrt{\frac{L}{g}}$$

Where:

$L$ is the length of the pendulum string or rod.

$g$ is the acceleration due to gravity.

Why it happens in summer:

Thermal Expansion: During the hot summer months, the metallic rod of the pendulum expands due to the increase in temperature, causing its length ($L$) to increase.

Longer Time Period: According to the formula, if the length ($L$) increases, the time period ($T$) also increases. This means each single swing takes slightly more time to complete.

Clock Runs Slow: Because every swing takes longer than it is supposed to, the clock registers fewer seconds than actual time has passed, causing it to lose time and run slow.

Why the Other Options Are Incorrect

Option 1: The actual length of a 24-hour solar day does not dictate the physical mechanics of a mechanical clock mechanism.

Option 2: While friction exists, it reduces the amplitude (width) of the swing rather than altering the core time period, and it doesn't systematically increase just because it is summer.

Option 4: The mass or weight of the pendulum bob has absolutely no effect on the time period ($T$ is completely independent of mass).