In what time (in seconds) will a train that is 100 metres long, running at a speed of 50 km/hr, completely cross a stationary pillar standing beside the track?

Introduction / Context:
This question is a straightforward application of the distance–speed–time relationship for trains. When a train crosses a pillar (or any stationary point), the distance covered for the purpose of the crossing is simply the length of the train itself. The problem checks your ability to convert units correctly and apply the basic formula time = distance / speed.

Given Data / Assumptions:
- Length of the train = 100 m.
- Speed of the train = 50 km/hr.
- The pillar is considered a point object with negligible width.
- The train travels at a uniform speed without acceleration or braking.

Concept / Approach:
To find the time taken for the train to pass a pillar, we use the fact that the train must move a distance equal to its own length. Since the speed is given in km/hr and the length is in metres, we must convert the speed into metres per second. Then, applying time = distance / speed gives us the crossing time in seconds.

Step-by-Step Solution:
Step 1: Distance relevant for crossing a pillar = length of the train = 100 m.Step 2: Convert 50 km/hr into m/s using the factor 5 / 18.Step 3: Speed in m/s = 50 * (5 / 18) = 250 / 18 = 125 / 9 m/s.Step 4: Use the time formula: time = distance / speed = 100 / (125 / 9) seconds.Step 5: Simplify: 100 / (125 / 9) = 100 * 9 / 125 = 900 / 125.Step 6: Divide numerator and denominator by 25: 900 / 125 = 36 / 5 = 7.2 seconds.Step 7: Thus, the train takes 7.2 seconds to completely cross the pillar.

Verification / Alternative check:
We can approximate to feel if the answer is reasonable. 50 km/hr is about 13.89 m/s. If the train travels at roughly 14 m/s, then to cover 100 m it would take about 100 / 14 ≈ 7.14 seconds, which is very close to 7.2 seconds. This confirms that the computed value is realistic and accurate.

Why Other Options Are Wrong:
7.0 seconds and 6.8 seconds are close but slightly smaller than the correct 7.2 seconds and result from rounding or ignoring exact conversion factors. 72 seconds and 70 seconds are far too large and would correspond to extremely slow speeds (much less than walking speed). Only 7.2 seconds matches the correct calculation with proper unit conversion.

Common Pitfalls:
Many students forget to convert km/hr to m/s and directly divide metres by km/hr, which mixes units and produces incorrect answers. Others mistakenly use the length of some imagined platform instead of just the train length when the object is a pillar. Always remember: crossing a point object involves only the train's length.

Final Answer:
The 100 metre long train will cross the pillar completely in 7.2 seconds.