Question

A student performs an experiment to determine the acceleration due to gravity $g$. The student throws a steel ball up with initial velocity $u$ and measures the height $h$ travelled by it at different times $t$. The graph the student should plot on a graph paper to readily obtain the value of $g$ is

• A. $h$ versus $t$
• B. $h$ versus $t^{2}$
• C. $h$ versus $\sqrt{t}$
• D. $h /t$ versus $t$

Answer 1

Answer: (D)

For thrown ball
$h=ut- \frac{1}{2}gt^{2} $
$\Rightarrow \frac{h}{t} =u -\frac{1}{2}gt$
$\Rightarrow \frac{h}{t} =\frac{-g}{2} .t +u $
Comparing with $y = mx + c,$
graph of $\frac{h}{t} h$ versus $t$ is a straight line with slope $\frac{-g}{2} $

From above graph, value of acceleration due to gravity can be obtained by multiplying its slope with $2$.