Question

kinetic energy of a moving body may depends upon its mass (m) and speed (v) . use method of dimensional analysis derive the relationship among them?

Answer 1

Explanation:

Since we  know that,

The dimension of energy [E]=[M1L2T−2]

The dimension of mass   [M]=[M1L0T0]

Dimension of velocity[V]=[M0L1T−1]

Let [E]=k[M]x[V]y

Where k is the proportionality constant which is a dimensionless quantity.

Therefore,

[M1L2T−2]=k[M1L0T0]x[M0L1T−1]y

So, x=1,y=2

Thus, We have

E=kmv2

It is found that k=21

Hence, E=21mv2

Answer 2

Since we know that,

The dimension of energy [E]=[M
1
L
2
T
−2
]
The dimension of mass [M]=[M
1
L
0
T
0
]
Dimension of velocity[V]=[M
0
L
1
T
−1
]

Let [E]=k[M]
x
[V]
y


Where k is the proportionality constant which is a dimensionless quantity.
Therefore,
[M
1
L
2
T
−2
]=k[M
1
L
0
T
0
]
x
[M
0
L
1
T
−1
]
y


So, x=1,y=2

Thus, We have
E=kmv
2


It is found that k=
2
1
​


Hence, E=
2
1
​
mv
2