On the surface of earth acceleration due to gravity is g and gravitational potential is V. Match the Column I with Column II and mark the correct option from the codes given below.Column $$I(A)$$ At height h $$=$$ R, value of $$g(B)$$ At depth h $$=$$ $$R2$$, value of $$g(C)$$ At height h $$=$$ R, value of $$V(D)$$ At depth h $$=$$ $$R2$$, value of V Column $$II(p)$$ decreases by a factor $$14(q)$$ decrease by a factor $$12(r)$$ decrease by a factor $$118(s)$$ increases by a factor $$2(t)$$ None

Question

On the surface of earth acceleration due to gravity is g and gravitational potential is V. Match the Column I with Column II and mark the correct option from the codes given below.Column $$I(A)$$ At height h $$=$$ R, value of $$g(B)$$ At depth h $$=$$ $$R2$$, value of $$g(C)$$ At height h $$=$$ R, value of $$V(D)$$ At depth h $$=$$ $$R2$$, value of V Column $$II(p)$$ decreases by a factor $$14(q)$$ decrease by a factor $$12(r)$$ decrease by a factor  $$118(s)$$ increases by a factor $$2(t)$$  None

Infinity Learn · Accepted Answer

As  $$g=GMR2$$,$$V=-GMRAt$$ height   $$h=R$$,$$g=g1+hR2=g4$$⇒V'$$=-GM2Ri$$.e. g decrease by a factor $$1/4$$ and V also decreases by a factor of $$1/2$$.At depth  $$h=R2g$$'$$=g1-hR=g1-12=g2V$$'$$=-GMR315R2-0.5r2=-GMR315R2-18R2=-118GMRi$$.e. g decrease by a factor $$12$$ and V' also decreases by a factor $$118$$.

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