First slide

Release from certain height

Question

Two bodies, A (of mass 1kg) and B (of mass 3kg) are dropped from heights of 16 m and 25 m, respectively. The ratio of the time taken by them to reach the ground is:

Moderate

A

5/4
B

12/5
C

5/12
D

4/5

Solution

For free fall from a height u=0 (initial velocity) By second equation of motion,
$h = ut + \frac{1}{2} {gt}^{2} = 0 + \frac{1}{2} {gt}^{2} \Rightarrow \frac{h_{1}}{h_{2}} = {(\frac{t_{1}}{t_{2}})}^{2}$
Given, h₁= 16 m, h₁= 25 m
$∴ \frac{t_{1}}{t_{2}} = \sqrt{\frac{h_{1}}{h_{2}}} = \sqrt{\frac{16}{25}} = \frac{4}{5}$

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