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2.Motion in Straight Line
normal
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 $t$
(KVPY-2017)
Solution
(d)
For thrown ball,
$h=u t-\frac{1}{2} g t^2 \Rightarrow \frac{h}{t}=u-\frac{1}{2} g t$
$\Rightarrow \quad \frac{h}{t}=\frac{-g}{2} \cdot t+u$
Comparing with $y=m x+c$, graph of $\frac{h}{t}$ 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 $2$ .
Standard 11
Physics
