1.

Find dimension of length if f force v velocity and t is time

Answer»

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


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