Physics · Motion In A Straight Line · NEET
The ruler is released from rest, so u = 0 and it is in free fall with acceleration g. From d = ut + (1/2) g t squared, with u = 0 you get d = (1/2) g t squared. Solving for time: t = sqrt(2d / g). Here d is the length of ruler that slips past before you catch it, and g = 9.8 m/s squared. This t is your reaction time.
Because your friend holds the ruler still and simply lets it go (drops it). At the moment of release its velocity is zero. So u = 0 always. This is the key that turns the general equation d = ut + (1/2) g t squared into the simple d = (1/2) g t squared. If the ruler were thrown down, u would not be zero and you could not use this shortcut.
Convert distance to metres: d = 21.0 cm = 0.21 m. Use t = sqrt(2d / g) = sqrt(2 x 0.21 / 9.8) = sqrt(0.42 / 9.8) = sqrt(0.0428) = 0.21 s (approximately). So the reaction time is about 0.21 seconds. Always change cm to m before putting numbers in, or your answer will be wrong by a factor.
A faster person catches the ruler sooner, so it falls a shorter distance. Since d = (1/2) g t squared, distance increases as reaction time increases. Smaller d means smaller t means quicker reflex. To rank people: the one with the smallest catch distance has the smallest (best) reaction time. Distance and reaction time follow the exact same order.
No. In free fall every object has the same acceleration g, independent of mass. So a heavy ruler and a light ruler fall the same distance in the same time. The reaction time depends only on how far the ruler slips (d) and on g, never on the ruler's mass. This is a common trap the exam uses.
A ruler is dropped vertically and five persons try to catch it. Their reaction times are A = 0.20 s, B = 0.22 s, C = 0.18 s, D = 0.19 s and E = 0.21 s. The correct order of the distance travelled by the ruler before being caught by each person is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Reaction time is the time a person takes to observe a situation, think, and then act. In the dropped ruler experiment it is the small delay between the ruler being released and you closing your fingers to catch it. It is typically about 0.2 seconds for most people.
Use g = 9.8 m/s squared unless the question gives a different value (some questions use 10 m/s squared to make the maths simple). Always read the question and use the g they provide.
No. These problems only use the kinematic equation d = (1/2) g t squared, rearranged to t = sqrt(2d / g). It is pure substitution once you convert the distance into metres.
Because the ruler falls under gravity alone, and gravity gives every object the same acceleration g. The only thing that changes the fall distance is how long you take to react. So the distance is a direct measure of your reaction time, not your grip strength or the ruler's weight.
