A cone falling with a speed `v_(0)` strikes and penetrates the block of a packing material. The acceleration of the cone after impact is `a=g-cx^(2)`. Where c is a positive constant and x is the penetration distance. If maximum penetration depth is `x_(m)` then c equalsA. `(2gx_(m)+v_(0)^(2))/(x_(m)^(2))`B. `(2gx_(m)-v_(0)^(2))/(x_(m)^(2))`C. `(6gx_(m)-3v_(0)^(2))/(2x_(m)^(3))`D. `(6gx_(m)+3v_(0)^(2))/(2x_(m)^(3))`

A cone falling with a speed `v_(0)` strikes and penetrates the block o

1.	A cone falling with a speed `v_(0)` strikes and penetrates the block of a packing material. The acceleration of the cone after impact is `a=g-cx^(2)`. Where c is a positive constant and x is the penetration distance. If maximum penetration depth is `x_(m)` then c equalsA. `(2gx_(m)+v_(0)^(2))/(x_(m)^(2))`B. `(2gx_(m)-v_(0)^(2))/(x_(m)^(2))`C. `(6gx_(m)-3v_(0)^(2))/(2x_(m)^(3))`D. `(6gx_(m)+3v_(0)^(2))/(2x_(m)^(3))`
Answer» Correct Answer - D `v(dv)/(dx)=g-cx^(2)` `impliesint_(v_(0))^(0)vdv=gint_(0)^(x)dx-cint_(0)^(x)x^(2)dx` `implies-(v_(0)^(2))/(2)=gx-(cx^(3))/(3)` `implies(x^(3)c)/(3)=gx+(v_(0)^(2))/(2)impliesc=(3g)/(x^(2))+(3v_(0)^(2))/(2x^(3))`

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