Question

The quantities A and B are related by the relation A/B = m, where m is the linear denaity and ,A is force, the dimwnsions of B will be​

Answer 1

Answer:

Required dimension formula for B is [ L^( 2 ) T^( - 2 ) ].

Explanation:

Given, A / B = m. It means that the dimensions A / B and m are equal.

Thus,

= > Dimension of A / B = Dimension of a

= > Dimension of A = Dimension of a x Dimension of B

= > Dimension of A / Dimension of a = Dimension of B

We know,

Dimension of A( force or ma ) = [ M L T^( - 2 ) ]

Dimension of a( linear mass density ) = [ M L^( - 1 ) ]

Therefore,

= > Dimension of B = [ M L T^( - 2 ) ] / [ M L^( - 1 ) ]

= > Dimension of B = [ L^{ 1- ( - 1 ) } T^( - 2 ) ]

= > Dimension of B = [ L^( 2 ) T^( - 2 ) ]

Hence the required dimension formula for B is [ L^( 2 ) T^( - 2 ) ].

Answer 2

Answer:

Explanation:

Given :-

A/B = m

A is force

m = linear density

________________________

We know that dimension formula :-

» A = Force = $ML{T}^{-2}$

» m = Linear density = $M{L}^{-1}{T}^{0}$

_________________________

__________________[ Put values]

Dimensions of B = A / m

B = $\large\frac{ML {T}^{ - 2} }{M {L}^{ - 1} {T}^{0} }$

________[After Solving]_______

» $\large \: \: {L}^{2}{T}^{ - 2}$

_______________________

So,the dimensions of B is

$\huge{L}^{2} {T}^{-2}$