Question

Find the dimensions of (a*b) in the equation E=a-x^2/bt
where E is energy. x is distance and t is time.​

Answer 1

Equation:-

$E= a - \frac{ {x}^{2} }{bt}$

By principle of homogeneity

Dimensions of E=a.

Therefore,

$E=a=M L {}^{2} T {}^{ - 2}$

then,

$E= \frac{ {x}^{2} }{bt}$

$b = \frac{ {x}^{2} }{Et}$

$b = \frac{ {L}^{2} }{ML {}^{2} T {}^{ - 2} \times \: T }$

$b =M {}^{ - 1} T \:$

Now dimensions of

$a \times b$

$ML {}^{2} T {}^{ - 2} × M {}^{ - 1} T \:$

$L {}^{2} T {}^{ - 1}$

so,the dimensions of a×b is

$L {}^{2} T {}^{ - 1} \:$