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 .

Options

A. `3.0 `cm
B. `2.5` cm
C. `2.0`cm
D. `1.5` cm

Answer

D

Explanation

Initial kinetic energy of bullet `= 1/2 mv_(0)^(2)`
The kinetic energy ,ehrn the velocity becomes half ` = (mv_(0)^(2))/8`
` :. K - K_(0) = W`
`(mv_(0)^(2))/8 -1/2 mv_(0)^(2) =Fd`
` = - 3/8 mv_(0)^(2)=F(6)`
` :. F = (mv_(0)^(2))/16`
Kinetic energy ,when the velocity become `1/4` th of intial velocity
` :. K = (mv_(0)^(2))/32`
` :. K - K = W`
` = (mv_(0)^(2))/32 = (mv_(0)^(2))/8 = Fd`
` = (3mv_(0)^(2))/32 = - (mv_(0)^(2))/16 d`
` : 3/2 = d`
` :. d = 1.5 cm `