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A bullet is fired into a huge wooden blo...

A bullet is fired into a huge wooden block . The bullet while moving inside the block loses half the velocity when it travles 6 cm inside the block . hOe far , then would it go inside the block ? And becomes rest .

Text Solution

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Suppose the intial kinetic energy of bullet ` = 1/2 mv_(0)^(2)`
when the velocity becomes halved the kinetic energy = `1/2 ((mv_(0)^(2))/4)`
According to work energy theorem ,
`W = DeltaK = K - K_(0)`
` :. F.d =1/2 ((mv_(0)^(2))/4)-1/2mv_(0)^(2)`
` :. F(6) =1/2 mv_(0)^(2) (1/4-1)`
`F(6) =-3/8 mv_(0)^(2)`
` :. F = - 1/16 mv_(0)^(2)`
If before coming to rest travels an additional distance d . Its kinetic energy becomes zero .
` :. Deltak =W`
` :. 0 -(mv_(0)^(2))/8 =[Fd] =-1/16 mv_(0)^(2) d`
` :. d = 2 cm `
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