The special theory of relativity reveals that the length of an object, moving with a speed close to the speed of light, appears shorter in length in the direction of motion. Prerna writes the relation that shows the extent of contraction of a rod as: $ L = L_0 \bigg( 1- \large\frac{1}{c^2} \bigg)^{\large\frac{1}{2}}$ Where, $c \rightarrow $ Speed of light, $L_0$ = Actual length, $L$ = Apparent length
Her sister Pooja tells her that this formula is dimensionally incorrect.
To make this relationship dimensionally correct, Prerna should