Question

Dimensional formula for
$f = at + bt^{2} + ct^{3}$
​

Answer 1

Answer:

[MLT

−3

] and [MLT

−4

]

⇒ Since F=at+bt

2

−−−(1)

∴ Dimension of at and bt

2

must be equal to force only.

Hence [F]=[M

1

L

1

T

−2

]−−−(2)

F from (1) and (2)

⇒ [at]=a[T]=[F]

∴ a[T]=[M

1

L

1

T

−2

]

∴ [a]=[M

1

L

1

T

−3

]

and per bt

2

=b[T

2

]=[M

1

L

1

T

−2

]

∴

[b]=[M

1

L

1

T

−4

]