A 500 m long train running at a speed of 100 m/s crosses a tunnel in 10 s. What is the length of the tunnel?

The correct option is 500 m.

When a train crosses a tunnel, the total distance covered by the train is equal to the sum of the length of the train and the length of the tunnel. We can represent this relationship as:

$\text{Total Distance}=\text{Length of Train}+\text{Length of Tunnel}$

Let us denote the length of the tunnel as $L$.

We are given the following parameters in the problem:
• Length of the train = 500 m
• Speed of the train = 100 m/s
• Time taken to cross the tunnel = 10 s

First, we calculate the total distance covered by the train using the speed-distance-time formula:

$\text{Distance}=\text{Speed}\times \text{Time}$

Substituting the given values into the formula:

$\text{Total Distance}=100\text{m/s}\times 10\text{s}=1000\text{m}$

Using the relation for total distance, we can solve for the tunnel length $L$ by substituting the known values:

$1000\text{m}=500\text{m}+L$

Subtracting the train length from the total distance gives:

$L=1000\text{m}-500\text{m}$

$L=500\text{m}$

Therefore, the length of the tunnel is 500 m.