Question

Find the velocity of bullet of mass 5g which is fired from a pistol of mass 1.5g. The recoil velocity of pistol is 1.5ms⁻¹. ​

Answer 1

Answer:

0.45m/s

Explanation:

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Answer 2

Mass of bullet (m$_a$) = 5 g

Mass of pistol (m$_b$) = 1.5 g

Initial velocity of pistol and bullet = 0 m/s

[u$_a$ = u$_b$ = 0]

Recoil velocity of pistol (v$_b$) = 1.5 m/s

Let recoil velocity of bullet = v

Law of conservation of Momentum:

The overal momentum before collision of 2 objects and after collision remains constant if no external unbalanced force acts on them.

Mathematically,

m$_a$u$_a$ + m$_b$u$_b$ = m$_a$v$_a$ + m$_b$v$_b$

$\therefore$ (5 g)(0 m/s) + (1.5 g)(0 m/s) = (5 g)v + (1.5 g)(1.5 m/s)

$\longrightarrow$ 5v + 2.25 = 0

$\longrightarrow$ 5v = - 2.25

$\longrightarrow$ v = - 0.45 m/s.

(Negative sign indicates the velocity of bullet is opposite to that of the pistol.)