Work Energy And Power Question 70

Question: An open knife edge of mass ’m’ is dropped from a height ‘h’ on a wooden floor. If the blade penetrates upto the depth ’d’ into the wood, the average resistance offered by the wood to the knife edge is [BHU 2002]

Options:

A) $ mg $

B) $ mg( 1-\frac{h}{d} ) $

C) $ mg( 1+\frac{h}{d} ) $

D) $ mg{{( 1+\frac{h}{d} )}^{2}} $

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Answer:

Correct Answer: C

Solution:

Let the blade stops at depth d into the wood. $ v^{2}=u^{2}+2aS $
therefore $ 0={{(\sqrt{2gh})}^{2}}+2(g-a)d $ by solving $ a=( 1+\frac{h}{d} )g $ So the resistance offered by the wood $ =mg( 1+\frac{h}{d} ) $



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