InterviewSolution
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InterviewSolution
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The masses and radii of the Earth and the Moon are `M_1, R_1 and M_2,R_2` respectively. Their centres are at a distance d apart. The minimum speed with which a particel of mass m should be projected from a point midway between the two centres so as to escape to infinity is ........A. `sqrt((2G(M_(1)+M_(2)))/d)`B. `sqrt((4G(M_(1)+M_(2)))/d)`C. `sqrt((4GM_(1)M_(2))/d)`D. `sqrt((G(M_(1)+M_(2)))/d)` |
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Answer» Correct Answer - B Potential energy of mass `m` when it is midway between masses `M_(1)` and `M_(2) ` is `U=-(GM_(1)m)/(d//2)-(GM_(2)m)/(d//2)=-(2Gm)/d(M_(1)+M_(2))` According to law of conservation of energy `1/2mv_(e)^(2)=(2Gm)/d(M_(1)+M_(2))` Therefore, escape velocity `v_(e)=sqrt((4G(M_(1)+M_(2)))/d)` |
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