The potential energy of the particle varies with distance ‘x’ as $straight U equals space fraction numerator Ax squared over denominator straight B squared plus straight x squared end fraction$ Find the dimensional formula of AB.

Solution

Given, x is the distance. Therefore the dimensional formula for 'x' is [L²]
Here, B²is added in X².
Therefore

space space space space space space space space space space space space straight B squared equals open square brackets straight L close square brackets squared rightwards double arrow space space space space space space space space straight B space equals space open square brackets straight L close square brackets space space Also comma space space space straight A equals fraction numerator straight B squared plus straight x squared over denominator straight x squared end fraction straight U

Thus the dimensional formula of AB is given by,

equals space open square brackets straight M to the power of 1 straight L squared straight T to the power of negative 2 end exponent close square brackets open square brackets straight L close square brackets space equals space open square brackets straight M to the power of 1 straight L cubed straight T to the power of negative 2 end exponent close square brackets

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