The answer is (b): 2.83 seconds, as can be seen by clicking your mouse on the photograph below.
The equation to determine how far an accelerated body moves as a function of time is:
where a is the acceleration.
The time for the accelerating body M to move the distance D between the two photocell gates due to the gravitational force on m is given by:
where g is the acceleration of gravity. Substituting 2M for M yields approximately t = sqrt(2)t0 or 2.83 seconds. Because M>>m, we have dropped the m from the numerator in the final relation for t0 in the equation above.
What error will this make in the final calculated value? The calculated time taken for mass m to accelerate mass M will be too short by the small fraction:
which is smaller than the experimental error in the apparatus.
