The gravitationasl fiedl in a region is given by `vecE=(5Nkg^-1)veci+(12nk^-1)vecj.`. a.find the magnitude of the gravitational force acting on a particle of mass 2 kg th gravittional fore actiing on a particle of mass 2 kg placed at the origin. B. Find the potential at teh points (12m,0) and (o,5m) if the potential at teh origin is taken to be zero. C. Find the change in gravitationa potential energyif a particle of mass 2 kg is taken from the origin to teh point (12m,5m). d. Find the change in potential energy if the particle is taken from (12m,0) to (0,5,m)`.

Answer

A, B, C, D

Explanation

`vecE=(5N/kg)veci+(12N/k)vecj`
a. `vecF=vecEm`
`=2kg[(5N/kg)veci(12N/kg)vecj]`
=(10N)veci+(24N)vecj`
`|vecF"|=sqrt(100+576)=sqrt676=26N`
b. `vecV=vecEr`
`At (12m, 0)=vecV=-(60J/kg)veci`
|vecV|=60J`
At `(0,5,m), vecV=-(60J/kgvecj)`,
`|vecV|=-60J`
c. `/_\V=int_(12,0)^(0,5) Emdr[(10N)veci+(24N)vecjr]`
`-(120vecjveci)+(120vecjveci)`
`=240j`
`d.` /_\V=-[R(10nveci+24Nvecj)]`
`=-120vec+120vecj=0`