Check the correctness of the relation U = mgh. Where U = potential energy , m = mass of the body , g = acceleration due to gravity and h = height of the body from the surface of the earth.
Answers
Step-by-step explanation:
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Step-by-step explanation:
Here we are given the expressions of kinetic energy and potential energy.
The expression for P.E is given as, P.E=mgh.
Let us first find the dimensional formula for potential energy for mgh
The mass,
m=[M]
Acceleration can be written as,
a=dt2
where d stands for the distance and t stands for the time.
The dimensional formula for acceleration can be written as,
a=LT2=LT−2
The dimensional formula for the acceleration due to gravity is, therefore,
g=[LT−2]
The dimensional formula for height
h=[L]
The dimensional formula for mgh can be written as,
mgh=[ML2T−2]
The dimensional formula for 12mv2 can be written as,
m=[M]
The formula for velocity
v=dt
where d stands for the displacement and t stands for time.
The dimensional formula for velocity will be
v=dt=LT=LT−1
Therefore,
v2=L2T−2
The dimensional formula for 12mv2 can be written as,
12mv2=[ML2T−2]
The dimensions of both 12mv2 and mgh are the same.
Therefore we can say that the relation mgh=12mv2 is dimensionally correct.
Hope it helps you