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2022 WAEC Physics Theory The effective potential energy, E, of a lunar satellite of mass, m, moving in an....

Physics
WAEC 2022

The effective potential energy, E, of a lunar satellite of mass, m, moving in an. elliptical orbit around the moon of mass, m, is given by

E = \(\frac{K^{2}}{2m_{1}r^{2}} - \frac{Gm_{1}m_{2}}{r}\) where r is the distance of the satellite from the mooń and G is the universal gravitational constant of dimensions, M\(^{-1}\)L\(^{3}\)T\(^{2}\).

Ďetermine the dimensions of the angular momentum, K, of the satellite using dimensional analysis.

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Explanation

Dimensions of the angular momentum, K =

\(\frac{[K]^{2}}{[m_{1}][r]^{2}} = \frac{[G][m_{1}][m_{2}]}{[r]}\)

\(\frac{[k]^{2}}{ML^{2}} = \frac{M^{-1} L^{3} T^{-2}M^{2}}{L}\)

[K] = (M\(^{2}\)L4T\(^{-2}\))½

\(\therefore\) [k] = ML\(^{2}T^{-1}\)


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WAEC Past Questions, Objective & Theory, Study 100% offline, Download app now - 24709
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WAEC May/June 2024 - Practice for Objective & Theory - From 1988 till date, download app now - 99995
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