A car is moving along a circular road of radius r with a uniform speed v has an acceleration a=v²/r. is the relation dimentionally correct.
Answers
Answer:
dimension of acceleration is given by
a=v/t
and
v=s/t
v=L/T= LT-¹
a=LT‐1/T= LT‐²
now for your formula
a=v²/r
a= (LT‐¹)²/L
a=L²T-²/L
a=LT‐²
which is dinemtionally correct
The relation a=v²/r is dimensionally correct.
Given:
A relation a=v²/r
To Find:
We are required to check whether the relation is dimensionally correct or not.
Solution:
The relation is dimensionally correct if both the L.H.S and R.H.S dimension formulas of the relation are equal.
The given relation is a = v²/r
L.H.S = a(acceleration)
The dimensional formula of acceleration(a) is given by, [M⁰ L¹ T⁻²].
L.H.S = [M⁰ L¹ T⁻²] -------(1)
R.H.S = v²/r -------(2)
The dimensional formula of velocity(v) is given by, [M⁰ L¹ T⁻¹].
The dimensional formula of radius(r) is given by, [M⁰ L¹ T⁰].
On substituting the dimensional formulas of velocity(v) and radius(r) in equation(2) we get
R.H.S = v²/r
R.H.S = [M⁰ L² T⁻²]/[M⁰ L¹ T⁰]
R.H.S = [M⁰ L²⁻¹ T⁻²⁻⁰]
R.H.S = [M⁰ L¹ T⁻²] -------(3)
From equation(1) and equation(3)
⇒ L.H.S = R.H.S
Therefore, The relation a=v²/r is dimensionally correct.
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