Check dimensionally the equation s=1/2gt²for a body falling freely under gravity and the equation v=underoot T/m for the speed of a transverse wave in a wire
Answers
Explanation:
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We know, one of the fundamental equation of motion is
v²-u²=2as
Where, v is Final Velocity
u is Initial Velocity
a is Acceleration
t is time taken.
In case of motion under gravity, the acceleration a and the distance s in the above equations are replaced by gravity g and the height of the object.
Thus the acceleration due to gravity equation is,
v²-u²=2gh
Where,
h is Height from ground level and
g is acceleration due to gravity.
For a body falling under gravity initially at rest i.e. u = 0, hence
v²=2gh
v=√2gh
⇒ v∝√gh