An open knife edge of mass m is droped from a height h on a wooden floor. If the blade penetrates a distance 'd' into the wood, then the average resistance offered by wood, to the blade is?
A
mg(1−hd)
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B
mg
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C
mg(1+hd)2
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D
mg(1+hd)
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Solution
The correct option is Cmg(1+hd) The resistive force FR exerted by wooden floor on the blade of the knife opposes the weight of the knife. So, the work done in penetrating a distance d is equal to the change in kinetic energy ∴W=(FR=mg)d=Kf−Ki ⇒(FR−mg)d=12mv2−0 ⇒(FR−mg)d=12m(2gh) ⇒FR−mg=mghd ⇒FR=mg(1+hd).