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Question

An object of mass 'm' is raised to height 'H' from the ground and released from there, prove that it's total mechanical energy remains same -
(i) At the lowest point
(ii) At height H/4 from the ground

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Solution

Dear Student ,
When the body of mass m is raised to height H then the total mechanical energy is the sum of the kinetic and potential energy .So at this point potential energy= mgHkinetic energy=0So total mechanical energy=mgHNow at the lowest point , kinetic energy=mgH (as the total potential energy is converted in to kinetic energy) .So the total mechanical energy at the lowest point = mgHNow at the height H2 ,potential energy=mgH2 and kinetic energy=12mv2=12m×2gH2=mgH2So the sum of the kinetic energy and potential energy is the total mechanical energy=mgH2+mgH2=mgHSo at height H2 and at the heighest point and at the lowest pint the total mechanical energy remains same .

Regards

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