The Question is from Physics Work energy power Law of conservation of energy, and it was created by the author Mr. ANIL KUMAR.G

Question

A body of mass M is dropped from a height h on a sand floor. If the body penetrates x cm into the sand, the average resistance offered by the sand to the body is

Mr. ANIL KUMAR.G · Accepted Answer

If the body strikes the sand floor with a velocity v, then $M{\rm{g}}h = \frac{1}{2}m{v^2}$ With this velocity v, when body passes through the sand floor it comes to rest after travelling a distance x. Let F be the resisting force acting on the body. Net force in downwards direction $ = M{\rm{g}} - F$ Work done by all the forces is equal to change in KE. $\left( {M{\rm{g}} - F} \right)x = 0 - \frac{1}{2}M{v^2}\,,\,\left( {M{\rm{g}} - F} \right)x = - M{\rm{g}}h\,or\,Fx = M{\rm{g}}h + M{\rm{g}}x$ or $F = M{\rm{g}}\left( {1 + \frac{h}{x}} \right)$

Mr. ANIL KUMAR.G · Answer

$M{\rm{g}}\left( {\frac{h}{x}} \right)$

Mr. ANIL KUMAR.G · Answer

The correct Option is "$M{\rm{g}}\left( {1 + \frac{h}{x}} \right)$"

Mr. ANIL KUMAR.G · Answer

$M{\rm{g}}h + M{\rm{g}}x$

Mr. ANIL KUMAR.G · Answer

$M{\rm{g}}\left( {1 - \frac{h}{x}} \right)$

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