Question

A body is projected vertically upwards from the surface of the earth with a velocity equal to ${\frac{3}{4}}^{th}$ escape velocity of earth. If ${}^{\prime }{R}^{\prime }$ is the radius of earth, the maximum height attained by the body is:

• A. $\frac{9}{7}R$
• B. $\frac{9}{8}R$
• C. $\frac{10}{3}R$
• D. $\frac{10}{9}R$

Answer 1

Answer: (A)

$\frac{9}{7}R$

Let us solve this problem using energy conservation,

$\frac{1}{2}m{\left(\frac{3}{4}{v}_e\right)}^2=\frac{GMm}{R}-\frac{GMm}{h}$

$\frac{1}{2}m\left(\frac{9GM}{8R}\right)=\frac{GMm}{R}-\frac{GMm}{h}$

$h=\frac{16}{7}R$

Height from surface of earth will be

$h^{\prime }=h-R=\frac{16}{7}R-R=\frac{9}{7}R$