Question

find k.E of an object is proportional to mass (A) , velocity (B) & acceleration (C) and also apply principle of homogeneity in it​

Answer 1

Answer:

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