JEE Physics 2023 Question with Solution

Given: Train A moves with speed $90 \, \text{km/h}$, train B moves in the opposite direction with speed $54 \, \text{km/h}$, and the observation time is $8 \, \text{s}$.

Find: The length of train B.

Convert the given speeds into SI units:

$$V_A = 90 \, \text{km/h} = 25 \, \text{m/s}$$ $$V_B = 54 \, \text{km/h} = 15 \, \text{m/s}$$

Since the trains are moving in opposite directions, the relative speed is:

$$V_{BA} = V_A + V_B = 25 + 15 = 40 \, \text{m/s}$$

For a passenger in train A, train B crosses with relative speed $V_{BA}$, so:

$$t = \frac{\ell}{V_{BA}}$$

Substitute the values:

$$8 = \frac{\ell}{40}$$

Hence,

$$\ell = 8 \times 40 = 320 \, \text{m}$$

Therefore, the length of train B is $320 \, \text{m}$. The working gives option C, although the solution incorrectly states option B.

Given: Opposite-direction motion of two trains and crossing time $8 \, \text{s}$.

Find: Length of train B.

When two objects move in opposite directions, their relative speed is the sum of their speeds. Convert mentally:

• $90 \, \text{km/h} = 25 \, \text{m/s}$
• $54 \, \text{km/h} = 15 \, \text{m/s}$

So the relative speed is:

$$40 \, \text{m/s}$$

Now use:

$$\text{length} = \text{relative speed} \times \text{time}$$

Thus,

$$\ell = 40 \times 8 = 320 \, \text{m}$$

Therefore, the correct option by calculation is C.