Ratio of Free Fall Times – Rankers Physics

Motion Under Gravity: Practice Problem & Solution

Two bodies, A (of mass \(1\text{ kg}\)) and B (of mass \(3\text{ kg}\)) are dropped from heights of \(16\text{ m}\) and \(25\text{ m}\), respectively. The ratio of the time taken by them to reach the ground is: [2006]
\(5/4\)
\(8/5\)
\(5/8\)
\(4/5\)

Solution Explained:

To solve this problem, we apply the core principles of Motion Under Gravity. Understanding the underlying formula is key to arriving at the correct answer below:

Concept: Free fall under gravity.
Formula: Distance \(h = \frac{1}{2}gt^2\) ⇒ time \(t = \sqrt{\frac{2h}{g}}\), so \(t \propto \sqrt{h}\)
For body A, \(h_A = 16\text{ m}\); for body B, \(h_B = 25\text{ m}\).
Ratio: \(t_A/t_B = \sqrt{h_A/h_B} = \sqrt{16/25} = 4/5\).

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