Question

A body is projected up with a velocity equal to $3/4$ th of the escape velocity from the surface of the earth. The height reached by the body above the earth's surface is: (Radius of the earth is $R$)

• A. $10R/9$
• B. $9R/7$
• C. $9R/8$
• D. $10R/3$

Answer 1

The correct option is B $9R/7$

Escape velocity, $V_s=\sqrt{\frac{2GM}{r}}$, where $r$ is height from centre of gravity
$V=\frac{3}{4}{V}_s=\frac{3}{4}\sqrt{\frac{2GM}{r}}$

By conservation of energy:
$K.E_i+P.E_i=K.E_f+P.E_f$
Hence, $\frac{9GMm}{16R}-\frac{GMm}{R}=0-\frac{GMm}{(R+h)}$

Thus, $h=\frac{9R}{7}$