Question

The escape velocity from a planet is $v_e$. A tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet, its speed will be

• A. $\frac{u}{\sqrt{2}}$
• B. $u$
• C. $\frac{u}{2\sqrt{2}}$
• D. $\frac{u}{2}$

Answer 1

Answer: (A), (B)

The correct options are
A $\frac{u}{\sqrt{2}}$
B $u$

$\frac{1}{2}m{v}_e^2=\frac{GMm}{R};v_e=\sqrt{\frac{GMm}{R}}=\sqrt{2gR}$
In tunnel body will perform $SHM$ at centre
$V_{max}=A\omega$
$=\frac{R2\pi }{2\pi \sqrt{R/g}}=\sqrt{gR}=\frac{v_e}{\sqrt{2}}$