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PhysicsKinematics
When a ruler falls vertically, 5 different persons catch it with different reaction times. (g = 9·8 m s⁻²)
A. Person A has reaction time of 0·20 s.
B. Person B has reaction time of 0·22 s.
C. Person C has reaction time of 0·18 s.
D. Person D has reaction time of 0·19 s.
E. Person E has reaction time of 0·21 s.
What is the correct order of the distance travelled by the ruler for each person?
Options
1
B > E > A > C > D
2
C > D > A > B > E
3
B > E > A > D > C
4
C > D > A > E > B
Correct Answer
Option 3 : B > E > A > D > C
Step-by-Step Solution
1

Key concept: Ruler falls from rest under gravity. Distance fallen = ½gt². Longer reaction time → ruler falls longer → greater distance.

So: Rank by reaction time (longest first) = rank by distance (greatest first)

2

Rank reaction times (descending):

PersonReaction TimeRank
B0.22 s1st (most distance)
E0.21 s2nd
A0.20 s3rd
D0.19 s4th
C0.18 s5th (least distance)
3

Order: B > E > A > D > C ✓

C has the fastest reaction (0.18s) → catches earliest → ruler falls least distance. B has slowest reaction (0.22s) → ruler falls most.

Theory: Free Fall & Kinematics
1. Free Fall Equations

When a ruler is dropped (initial velocity u = 0), it falls under gravity alone. The kinematic equations simplify to:

v = gt

d = ½gt²

v² = 2gd

Here g = 9.8 m/s² ≈ 10 m/s² (for approximate calculations). The key relationship is d ∝ t² — distance increases as the square of time. A person with twice the reaction time catches the ruler after it has fallen 4 times the distance!

2. Actual Distances in This Problem

📌 C (0.18s): d = ½×9.8×0.18² = 0.159 m ≈ 15.9 cm

📌 D (0.19s): d = ½×9.8×0.19² = 0.177 m ≈ 17.7 cm

📌 A (0.20s): d = ½×9.8×0.20² = 0.196 m ≈ 19.6 cm

📌 E (0.21s): d = ½×9.8×0.21² = 0.216 m ≈ 21.6 cm

📌 B (0.22s): d = ½×9.8×0.22² = 0.237 m ≈ 23.7 cm

All within a 8 cm range! Typical human reaction time is 150–300 ms (0.15–0.30 s), corresponding to ruler falling 11–44 cm. This is a classic experiment in school physics labs to measure reaction time.

3. Equations of Motion

For motion with constant acceleration a, starting with initial velocity u:

v = u + at

s = ut + ½at²

v² = u² + 2as

For free fall: u = 0, a = g. These give v = gt, s = ½gt², v² = 2gs. Acceleration due to gravity g = 9.8 m/s² (use 10 m/s² for quick NEET calculations unless specified).

4. Projectile Motion Key Points

📌 Horizontal: no acceleration, x = u_x × t

📌 Vertical: acceleration = g downward, y = u_y t − ½gt²

📌 Time of flight: T = 2u sinθ/g

📌 Max height: H = u²sin²θ/2g

📌 Range: R = u²sin2θ/g (max at θ = 45°)

5. Reaction Time Measurement

This experiment uses free fall to measure human reaction time. When the ruler is released, the person catches it as fast as possible. Measuring the length of ruler that fell (d), reaction time t = √(2d/g). Typical results: 150–250 ms for young people. Athletes and gamers may have 120–150 ms. Older people may have 250–400 ms. This is a standard NEET practical experiment.

Frequently Asked Questions
1. Why does longer reaction time → greater distance? ⌄
d = ½gt². As t increases, d increases (proportional to t²). The longer a person takes to react, the more time the ruler has to accelerate under gravity, so it falls farther before being caught.
2. Who has the best (fastest) reaction time? ⌄
Person C with 0.18 s. Fastest reaction = shortest time = smallest distance fallen. C catches the ruler when it has fallen only about 15.9 cm — the shortest drop of all five persons.
3. Why is d ∝ t² and not d ∝ t? ⌄
Because d = ½gt² — this is quadratic in t, not linear. The ruler is accelerating (not moving at constant speed). If it moved at constant speed, d would be proportional to t. Since gravity accelerates it, it moves faster and faster, covering more distance per second as time goes on.
4. How far does the ruler fall in 0.22 s? ⌄
d = ½ × 9.8 × (0.22)² = 4.9 × 0.0484 = 0.237 m ≈ 23.7 cm. Person B catches the ruler after it falls about 24 cm — the greatest drop among the five.
5. What is the velocity of ruler when C catches it? ⌄
v = gt = 9.8 × 0.18 = 1.764 m/s ≈ 1.76 m/s for person C. For B: v = 9.8 × 0.22 = 2.156 m/s. The ruler hits harder (faster) when reaction time is longer — important for sports and safety applications.
6. Does mass of ruler affect how fast it falls? ⌄
No. In free fall, all objects fall with the same acceleration g regardless of mass (Galileo's famous result). A heavy steel ruler and a light plastic ruler fall at exactly the same rate in the absence of air resistance.
7. What is the third kinematic equation v² = 2gd used for here? ⌄
We can find velocity without knowing time: v = √(2gd). For person A: d = 19.6 cm = 0.196 m. v = √(2×9.8×0.196) = √(3.84) = 1.96 m/s. This also equals gt = 9.8×0.20 = 1.96 m/s ✓.
8. What is the difference in distance between B and C? ⌄
d_B = 23.7 cm, d_C = 15.9 cm. Difference = 7.8 cm. Despite only a 0.04 s difference in reaction time (40 ms!), the ruler falls 7.8 cm more. This shows how sensitive the ruler-drop experiment is to small differences in reaction time.
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