Question

A group of students is designing an experiment to verify earth's freefall acceleration rate. They plan to evacuate the air from a bell jar using a vacuum pump, and then use a remotely controlled apparatus within the vacuum to drop a spherical metal object from rest. The group does not have a means to directly measure the sphere's acceleration rate, so they instead plan to measure other quantities about the sphere and its motion, and then will calculate an experimental value for acceleration.
Which one of the following options of measurements would provide the group with enough information to determine the sphere's acceleration rate, without making any unnecessary additional measurement?

• A. Only the drop height of the sphere
• B. Both the drop height and the fall time of the sphere
• C. The drop height, fall time, and mass of the sphere
• D. The drop height, fall time, and landing speed of the sphere

Answer 1

Answer: (B)

Both the drop height and the fall time of the sphere

When an object is dropped under gravity, the loss in gravitational potential is equal to the gain in kinetic energy.

Hence $mgh=\frac{1}{2}m{v}^2$

$⟹g=\frac{v^2}{2h}$

There is another way to measure too.

we know that

$h=\frac{1}{2}g{t}^2$

$⟹g=\frac{2h}{t^2}$

Hence correct answer is option B.