Question

Two projectiles of same mass have their maximum kinetic energies in the ratio 4 : 1 and the ratio of their maximum height is also 4 : 1 .Then the ratio of their range is

• A. 2 : 1
• B. 4 : 1
• C. 8 : 1
• D. 16 : 1

Answer 1

The correct option is B 4 : 1

Maximum height attained $H=\frac{u^2{\sin }^2\theta }{2g}$
We get $H=\frac{K.E{\sin }^2\theta }{mg}$
where $K.E=\frac{1}{2}m{u}^2$
$⟹$ $\frac{H_2}{H_1}=\frac{K.E_2}{K.E_1}\frac{{\sin }^2{\theta }_2}{{\sin }^2{\theta }_1}$ $(\because m_1=m_2)$
Or $\frac{4}{1}=\frac{4}{1}\frac{{\sin }^2{\theta }_2}{{\sin }^2{\theta }_1}$
$⟹{\theta }_2={\theta }_1$
Range $R=\frac{u^2\sin 2\theta }{g}=\frac{2K.E\sin 2\theta }{gm}$
We know ${\theta }_2={\theta }_1$ $m_2=m_1$
$⟹$ $\frac{R_2}{R_1}=\frac{K.E_2}{K.E_1}=\frac{4}{1}$