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A physics experiment involves determining the acceleration due to gravity $(g)$ using a free-fall apparatus. An object is dropped from a known height $(h)$ of $2\ m$ above the ground. The time (t) taken for the object to reach the ground is measured. Calculate the acceleration due to gravity.
Option: 1
$9.7656\ m/s^{2}$

Option: 2
$9.365\ m/s^{2}$

Option: 3
$9.8145\ m/s^{2}$

Option: 4
$9.8255\ m/s^{2}$

Answers (1)

best_answer

Given values:
• Height $(h)=2\ m$
• Time $(t)=0.64\ s$
The equation of motion for free fall relates the height, time, and acceleration
due to gravity:

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

Solve for $g$ :

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

Step 1: Substitute the given values and calculate the acceleration due to
gravity $(g)$ :

$g=\frac{2 \times 2 \mathrm{~m}}{(0.64 \mathrm{~s})^2}$

Step 2: Calculate $g$ :

$\begin{gathered} g=\frac{8 \mathrm{~m}}{0.4096 \mathrm{~s}^2} \\ g \approx 19.536 \mathrm{~m} / \mathrm{s}^2 \end{gathered}$

The acceleration due to gravity is approximately $9.7656 \ m/s^2$
.

Conclusion
The acceleration due to gravity is calculated to be approximately $19.536 \ m/s^2$
.

Therefore, the correct option is (A).

Posted by

Devendra Khairwa

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