Question

A tunnel is dug along a chord of the earth at a perpendicular distance R/3 from the earth’s centre. Assume wall of the tunnel is frictionless. Find the force exerted by the wall on mass m at a distance x from the centre of the tunnel.

• A. $\frac { m g \sqrt { \left( R ^ { 2 } / 9 \right) + x ^ { 2 } } } { R }$
• B.
• C. $\frac { \mathrm { mg } } { 3 }$
• D. $\frac { \mathrm { mgx } } { \mathrm { R } }$

Answer 1

Answer: (C)

$\frac { \mathrm { mg } } { 3 }$

Answer 2

F = mg' = mg $\left[ 1 - \frac { \sqrt { \left( \mathrm { R } ^ { 3 } / 9 \right) + \mathrm { x } ^ { 2 } } } { 9 } \right]$

= .