(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A pendulum having a bob of mass ##m## is hanging in a ship sailing along the equator from east to west. If the ship sails at speed v what is the tension in the string?. Angular speed of earth's rotation is ## \omega ## and radius of the earth is ## R ##

2. Relevant equations

## T = mg - R\omega'^2##

3. The attempt at a solution

If the ship were still, the tension in the string would be given by

## T_0 = mg - mR\omega^2##

However since the ship moves in the direction opposite to earths rotation, the angular velocity of earth with respect to the ship would be ## \omega + \frac{v}{R}##

Therefore the tension would be

## T = mg - mR(\omega + \frac{v}{R})^2 \\

T \approx T_0 - 2m\omega v

##

Doubt:The answer key says that ## T \approx T_0 + 2m\omega v ## which means the relative angular velocity was taken as ## \omega - \frac{v}{R} ## . But isn't that the relative angular velocity when the ship sails from west to east. Where did I go wrong?

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# Homework Help: Gravitation and a Pendulum

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