Question

A bullet of mass $50g$ moving with an initial velocity of $\sf 100{ms}^{-1}$, strikes a wooden block and comes to rest after penetrating a distance $2 cm$ in it.

Calculate :

$\text{(i) Initial momentum of the bullet.}$
$\text{(ii) Final momentum of the bullet.}$
$\text{ (iii) Retardation caused by the wooden block}$
$\text{ (iv) Resistive force exerted by the wooden block.}$

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Answer 1

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Answer 2

Given :

➳ Mass of bullet = 50g = 0.05kg

➳ Initial velocity = 100m/s

➳ Distance covered = 2cm = 0.02m

➳ Final velocity = zero (i.e., rest)

To Find :

⟶ Initial momentum of bullet.

⟶ Final momentum of bullet.

⟶ Retardation caused by block.

⟶ Resistive force exerted by block.

SoluTion :

⇒ Momentum is defined as the product of mass and velocity.

• P = m × v

✴ Initial momentum :

$\implies\tt\:P_i=m\times u$

$\implies\tt\:P_i=0.05\times 100$

$\implies\boxed{\bf{P_i=5\:Ns}}$

✴ Final momentum :

$\implies\tt\:P_f=m\times v$

$\implies\tt\:P_f=0.05\times 0$

$\implies\boxed{\bf{P_f=0\:Ns}}$

✴ Retardation :

$\implies\tt\:v^2-u^2=2as$

$\implies\tt\:(0)^2-(100)^2=2a(0.02)$

$\implies\tt\:a=-\dfrac{10000}{2\times 0.02}$

$\implies\boxed{\bf{a=-250000\:ms^{-2}}}$

✴ Resistive force :

$\implies\tt\:F=m\times a$

$\implies\tt\:F=0.05\times 250000$

$\implies\boxed{\bf{F=-12500\:N}}$

[Note : Negative sign shows that, Force exerts in negative direction of motion of bullet.]