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Olympiad workbook

Exam: Olympiad workbook
Subject: NSEP
Chapter: Gravitation

Olympiad workbook · NSEP · Gravitation

The figure shows a smooth tunnel AB( length =2 ) in a uniform...

The figure shows a smooth tunnel

\mathrm{AB}(

length

=2 \ell)

in a uniform density planet (say Earth) of mass

M

and radius

R

. A small ball of mass

m

is released from rest at the end

A

of the tunnel. Acceleration due to gravity at surface of the planet is g . Time taken by the ball to reach the end B is The figure shows a smooth tunnel AB( length =2 ) in a uniform density planet (say Earth) of mass M and radius R . A

The figure shows a smooth tunnel AB( length =2 ) in a uniform density planet (say Earth) of mass M and radius R . A

Options

A $\pi \sqrt{\frac{R}{g}}$
B $2 \sqrt{\frac{\ell}{g}}$
C $\frac{\pi}{2} \sqrt{\frac{2 R}{g}}$
D $2 \pi \sqrt{\frac{R}{g}}$

Correct answer

A. $\pi \sqrt{\frac{R}{g}}$

Step-by-step solution

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