Question

Solve this:
5 an object has a weight W newton on the surface of the earth.
(i) What will be the weight of the object if it is taken from the surface of the earth to the surface of the moon?
(ii) What angular speed of the earth will make the object fly off its surface?

Answer 1

Dear Student,

Weight W=Mg

where g is acceleration due to gravity on earth, M is the mass of the object

at moon g'=g/6 i.e g' at moon is 1/6 that of earth,

or, weight W'=Mg'$=\frac{Mg}{6}\Rightarrow \frac{W}{6}$
$$\begin{gathered} accelerationduetogravityofplanetisdependenttotheangularvelocityoftheplanet \\ bythefollowingrelation. \\ g\text{'}=g-R{\omega }^2{\cos }^2\phi \\ g\text{'}=g-R{\omega }^2{\cos }^2\phi \\ forg\text{'}tobe0 \\ R{\omega }^2{\cos }^2\phi =g \\ or,\omega =\sqrt{\frac{g}{R{\cos }^2\phi }} \\ soforangularspeed\omega >\sqrt{\frac{g}{R{\cos }^2\phi }}theobjectwillflyoff \\ assumingtheobjectisatequator,where\phi is=0or \\ \omega >\sqrt{\frac{g}{R}} \end{gathered}$$
Regards.