Question

The work done'W' by a body varies with displacement 'x' as w=Ax+B/(c-x)2.the dimensional formula for B

Answer 1

Answer:

[B]= ML^3T^-2

Explanation:

[W] = ML^2T^-2

[C]=[X]= L

so,

According to Homogeneity Principle,

Dimension of Work is equal to dimension of B/(c-x).

so on equating both sides,

we will get [B]

Answer 2

Given :

The work done'W' by a body varies with displacement 'x' as :

$W=Ax+\dfrac{B}{(c-x)^2}$

To Find :

The dimensional formula for B .

Solution :

We know , dimensional formula of work done is :

$W=[M\ L^2\ T^{-2}]$

Now , by rule of dimension rule .

Dimension of $\dfrac{B}{(c-x)^2}$ must be equal to the dimension of work .

Therefore ,

$\dfrac{B}{[L]^2}=[M\ L^2\ T^{-2}]\\\\B=[M\ L^4\ T^{-2}]$

Learn More :

Units and Dimensions

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