Which of the following is dimensionless?

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(D) dimensionless quantity is a quantity that has no physical dimension,meaning its dimensional formula is $M^0 L^0 T^0$.$1$. The dimension of Force i

Vedclass · Accepted Answer

$\frac{	ext{Energy}}{	ext{Work}}$

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(D) dimensionless quantity is a quantity that has no physical dimension,meaning its dimensional formula is $M^0 L^0 T^0$.$1$. The dimension of Force is $[MLT^{-2}]$ and Acceleration is $[LT^{-2}]$. Their ratio is $[M]$,which is not dimensionless.$2$. The dimension of Velocity is $[LT^{-1}]$ and Acceleration is $[LT^{-2}]$. Their ratio is $[T]$,which is not dimensionless.$3$. The dimension of Volume is $[L^3]$ and Area is $[L^2]$. Their ratio is $[L]$,which is not dimensionless.$4$. Both Energy and Work have the same dimensional formula,which is $[ML^2T^{-2}]$. Therefore,their ratio is $\frac{[ML^2T^{-2}]}{[ML^2T^{-2}]} = [M^0L^0T^0]$,which is dimensionless.Thus,the correct option is $D$.

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