a satellite of mass m revolving in circular orbit of radius r round the Earth of mass m has binding energy E the angular momentum of satellite will be
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Velocity VsVs of the satellite is given by
GMmsr2s=nsv2srsGMmsrs2=nsvs2rs
vs=(GMrs)−−−−−−−√vs=(GMrs)
KE=12msvs=12KE=12msvs=12ms(GMns)ms(GMns)
PE=−GMmsrsPE=−GMmsrs
EE Total energy =KE+PE=KE+PE-----(1)
=−GMms2rs=−GMms2rs
Angular momentum
L=msvsrsL=msvsrs
=ms(GMrs)1/2=ms(GMrs)1/2rsrs
=(GMm2srs)1/2=(GMms2rs)1/2
Substituting from (1)
L=(2Emsr2s)1/2L=(2Emsrs2)1/2
Hence a is the correct answer.
Velocity VsVs of the satellite is given by
GMmsr2s=nsv2srsGMmsrs2=nsvs2rs
vs=(GMrs)−−−−−−−√vs=(GMrs)
KE=12msvs=12KE=12msvs=12ms(GMns)ms(GMns)
PE=−GMmsrsPE=−GMmsrs
EE Total energy =KE+PE=KE+PE-----(1)
=−GMms2rs=−GMms2rs
Angular momentum
L=msvsrsL=msvsrs
=ms(GMrs)1/2=ms(GMrs)1/2rsrs
=(GMm2srs)1/2=(GMms2rs)1/2
Substituting from (1)
L=(2Emsr2s)1/2L=(2Emsrs2)1/2
Hence a is the correct answer.
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