Given below are two statements. One is labelled as Assertion A and...

Range of two balls are ${R}_{1} = \dfrac{{u}^{2}\sin 2{\theta}_{1}}{g} = {R}_{2} = \dfrac{{u}^{2}\sin 2{\theta}_{2}}{g}$.

Now, maximum height by both balls are ${h}_{1} = \dfrac{{u}^{2}\sin^{2}{\theta}_{1}}{2g}$ and ${h}_{2} = \dfrac{{u}^{2}\cos^{2}{\theta}_{2}}{2g}$

$∴ \sqrt{{h}_{1}{h}_{2}} = \left(\dfrac{{u}^{2}\sin^{2}\theta}{2g}\right)\left(\dfrac{{u}^{2}\cos^{2}\theta}{2g}\right) = \dfrac{{u}^{2}sin\theta cos\theta}{2g}$$= \dfrac{R}{4}$

${⇒ R = 4\sqrt{{h}_{1}{h}_{2}}}^{}$

Hence, both A and R are true and R is the correct explanation of A.