A bullet penetrates a distance d of a plank. If the initial momentum of the bullet is doubled, the distance penetrated will be
4d
d
2d
d2
A
d2
B
4d
C
2d
D
d
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Solution
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Initial momentum - p1
Final momentum - p2
Distance penetrated - x
p1=mv
v2=u2+2as
⇒02=v2−2ad; final velocity would be zero
⇒v=√2ad
Now, momentum becomes double
p2=2p1
⇒p2=2m√2ad
⇒P2=mv2
So,
v2=2√2ad
Now. again apply third equation of motion-
v2=u2+2as
⇒02=(2√2ad)2−2ax
⇒x=4d
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