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Question

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

A
Mg(hx)
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B
Mg(1+hx)
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C
Mgh+Mgx
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D
Mg(1hx)
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Solution

The correct option is B Mg(1+hx)
If the body strikes the sand floor with a velocity v, then
Mgh=12Mv2
Let F be the resisting force acting on the body. Then, the resultant force = Fmg
Using work-energy theorem
(FMg)x=12Mv2
(FMg)x=MghF=Mg(1+hx)
(b)

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