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The grvitationa potential in a region is...

The grvitationa potential in a region is given by 'V=20Nkg^-1(x+y)'. A. Show tht the equation is dimensionaslly correct b. Find lthe gravitational field at the point `(x,y)` Leave youranswer in terms of the unit vector `veci,vecj,veck`. C. Calculate the magnitude of the gravitational fore on a particle of mass 500 g placed at the origin.

Text Solution

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The correct Answer is:
A, B, C
a. `V=((20N)/(kg))(x+y)`
`(GM)/R=(MLT^-2)/M,L`
`or (M^-1L^3T^-2M^1)/L=(ML^2T^-2)/M`
`or (M^0L^2T^-2=M^0L^2T^-2`
`:.LHS=RHS`
`b. vecE_(x,y)-20(N/(kg))veci-((20N)/kg)vecj`
`c. vecF=vecEm`
`=0.5kg[-((20N)/kg)veci-((20N)/veckg)vecj]`
`=-(10N)veci-(10N)vecj`
`:.|vecF|=sqrt(100)+(100))`
`=10sqrt2N`
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