Question

Derive an expression for kinetic energy of a body of mass m moving with velocity v.​

Answer 1

Answer:

Explanation:

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