23P2Q03

3ai)

\displaystyle \begin{aligned}  (F&=G\frac{Mm}{{{r}^{2}}}) \\ F&=(6.67\times {{10}^{-11}})\frac{(6.0\times {{10}^{24}})(6800)}{{{[(6400+36000)\times {{10}^{3}}]}^{2}}} \\ &=1510\text{N} \end{aligned}

3aii)

\displaystyle \begin{aligned}  G\frac{Mm}{{{r}^{2}}}&=mr{{\omega }^{2}} \\ \omega & =\sqrt{\frac{GM}{{{r}^{3}}}} \end{aligned}

Not necessary.

Both the gravitational force and the required centripetal force are directly proportional to the mass.

For the same orbital radius, all satellites orbit at the same angular velocity (and thus period), regardless of the mass of the satellite.

3bi)

The magnetic force provides the required centripetal force for circular motion.

\displaystyle \begin{aligned}   Bqv&=m\frac{{{v}^{2}}}{r} \\  Bqr&=p \\  (1.8\times {{10}^{-3}})(1.60\times {{10}^{-19}})r&=(3.4\times {{10}^{-23}}) \\  r&=0.118\text{ m} \end{aligned}

3bii)

No.

If the ion has a different mass, it has a different momentum but experience the same magnetic force.

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