A pendulum having a bob of mas m is hanging in a ship sailing along the equator from east to west. When the ship is stationary with respect to water the tension in the string is `T_0`. a. Find the speed of the ship due to rotation of the earth about its axis. b. find the difference between `T_0` and the earth's attraction on the bob. c. 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.

Answer

A, B, C

Explanation

Speed of the ship due to rotation of earth
`v=omega R`
b. `T_0=mg-momega^2R`
`:. T_0-mg=momega^2R`
c. If the shipshifts at speed v
`T=mg-momega_1^2R`
`=T_0-((v-omegaR)^2)/R^2R`
`=T_0-((v^2+omega^2R^2-2omegaRv))/R R`
`:.T=T_0+2omeavm`