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Suppposing Netwon's law of gravitationa for gravitation forces overset rarr(F_(1)) and overset rarr(F_(2)) between two masses m_(1) and m_(2) at positions overset rarr(r_(1)) and oversetrarr(r_(2)) read oversetrarr(F_(1)) = - oversetrarr(F_(2)) = -(oversetrarrr_(12))/(r_(12)^(3)) GM_(0)^(2) ((m_(1)m_(2))/(M_(0)^(2)))^(n) where M_(0) is a constant of dimension of mass, oversetrarr(r_(12)) =oversetrarr(r_(1)) -oversetrarr(r_(2)) and n is a number. in such a case,

Answer» <html><body><p>the <a href="https://interviewquestions.tuteehub.com/tag/acceleration-13745" style="font-weight:bold;" target="_blank" title="Click to know more about ACCELERATION">ACCELERATION</a> <a href="https://interviewquestions.tuteehub.com/tag/due-433472" style="font-weight:bold;" target="_blank" title="Click to know more about DUE">DUE</a> to gravity on earth will be different for different objects.<br/>none of the three laws of kepler will be valid.<br/>only of the third law will become invalid.<br/>for `n` negative, an object ligther than water will sink in water.</p>Solution :`F = (r_(12))/(r_(12)^(<a href="https://interviewquestions.tuteehub.com/tag/13-271882" style="font-weight:bold;" target="_blank" title="Click to know more about 13">13</a>)) GM_(0)^(2) [(m_(1)m_(2))/(M_(0)^(2))]^(n) = (GM_(0)^(2(1 - n)))/(r_(12)^(12))(m_(1)m_(2))^(n)` <br/> Acceleration due to gravity, `g = (F)/(mass) = (GM_(0)^(2(1 - n)))/(r_(12)^(12)) ((m_(1)m_(2))^(n))/(mass)`<br/> Thus acceleration due to gravity on earth is different for different objects. In this situation Kepler's third law will not be valid. <br/> When `n` is negative, then <br/> `g = (GM_(0)^(2(1 + n)))/(r_(12)^(12)) ((m_(1)m_(2))^(-n))/(mass)` <br/> which is <a href="https://interviewquestions.tuteehub.com/tag/positive-1159908" style="font-weight:bold;" target="_blank" title="Click to know more about POSITIVE">POSITIVE</a> as `M_(0) gt m_(1)` or `m_(2)`. <br/> Therefore, object ligher than water will sink in water.</body></html>


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