question_answer

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]

A)             \[mg\]  

B)             \[mg\left( 1-\frac{h}{d} \right)\]

C)             \[mg\left( 1+\frac{h}{d} \right)\]

D)               \[mg{{\left( 1+\frac{h}{d} \right)}^{2}}\]

Correct Answer: C

Solution :

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