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A bullet fired into a fixed target loses...

A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm . How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?

A

3.0 cm

B

2.0 cm

C

1.5 cm

D

1.0 mc

Text Solution

Verified by Experts

The correct Answer is:
D
According to work-energy theorem,
Total work done = Change in kinetic energy
`W = Delta K`
Case I - `F xx 3 = 1/2 m ((v_0)/(2))^(2) - 1/2 m v_0^2`
Where, is resistive force and is initial speed.
Case II Let the further distance travelled by the bullet before coming to rest be s.
`:. - F (3 + s) = K_(f) - K_(i) = -1/2 mv_0^2" " implies -1/8 mv_0^2 (3 + s) = -1/2 mv_(0)^(2)`
or, `1/4 (3 + s) = 1 " or " 3/4 + s/4 = 1 " or " s = 1 cm`.
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