First slide

Dimensions of physical quantities

Question

The energy $E$ of an oscillating body in simple harmonic motion depends on its mass $m$ , frequency $n$ and amplitude $a$ . Using the method of dimensional analysis, find the relation analysis, find the relation between $E, m, n a n d a$ .

Moderate

A

x=-1, y=2, z=2
B

x=1, y=2, z=2
C

x=2, y=2, z=2
D

x=-2, y=2, z=2

Solution

$[E] = k [m]^{x} [n]^{y} [a]^{z}$
where, k is a dimensionless constant.
$∴ [{ML}^{2} T^{- 2}] = k [M]^{x} {[T^{- 1}]}^{y} [L]^{z}$
Solving, we get
x=1, y=2 and z=2
$∴ E = k m n^{2} a^{2}$

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