Question

Write dimensions of energy, if velocity force and time are taken as fundamental quantities






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Answer 1

Answer:

Let M = (some Number) (V)  

a

(F)  

b

(T)  

c

 

Equating dimensions of both the sides

M  

1

L  

0

T  

0

=(1)[L  

1

T  

−1

]  

a

[M  

1

L  

1

T  

−2

]  

b

[T  

1

]  

c

 

M  

1

L  

0

T  

0

=M  

b

L  

a+b

T  

−a−2b+c

 

get a = - 1, b = 1, c = 1

M = (Some Number) (V  

−1

F  

1

T  

1

)⇒[M]=[V  

−1

F  

1

T  

1

]

Similarly, we can also express energy in terms of V, F, T

Let [E] = [some Number] [V]  

a

[F]  

b

[T]  

c

 

⇒[ML  

2

T  

−2

]=[M  

0

L  

0

T  

0

][LT  

−1

]  

a

[MLT  

−2

]  

b

[T]  

c

 

[M  

1

L  

2

T  

−2

]=[M  

b

L  

a+b

T  

−a−2b+c

]

⇒ 1 = b; 2 = a + b ; -2 = -a - 2b + c

get a = 1 ; b = 1 ; c = 1

∴   E = (some Number) V  

1

F  

1

T  

1

or[E]=[V  

1

][F  

1

][T  

1

]

Explanation: