A particle of mass moving with velocity collides with a stationary particle of mass . After collision, they stick together and continue to move together with velocity ______. [2023]

Question

A particle of mass $m$ moving with velocity $v$ collides with a stationary particle of mass $2 m$ . After collision, they stick together and continue to move together with velocity ______. [2023]

Smart Achievers · Accepted Answer

(3)

$Applying conservation of linear momentum$

$\Rightarrow {\vec{P}}_{i} = {\vec{P}}_{f}$

$m v + 2 m \times 0 = (3 m) v'$

$∴$ $m v = 3 m v' \Rightarrow v' = \frac{v}{3}$

Solution

Q.
A particle of mass $m$ moving with velocity $v$ collides with a stationary particle of mass $2 m$ . After collision, they stick together and continue to move together with velocity ______. [2023]

1 $v$

2 $\frac{v}{2}$

3 $\frac{v}{3}$

4 $\frac{v}{4}$

Ans.
(3)

$Applying conservation of linear momentum$

$\Rightarrow {\vec{P}}_{i} = {\vec{P}}_{f}$

$m v + 2 m \times 0 = (3 m) v'$

$∴$ $m v = 3 m v' \Rightarrow v' = \frac{v}{3}$

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Solution

Q. A particle of mass m moving with velocity v collides with a stationary particle of mass 2m. After collision, they stick together and continue to move together with velocity ______. [2023]

1 v

2 v2

3 v3

4 v4

Ans. (3) Applying conservation of linear momentum ⇒P→i=P→f mv+2m×0=(3m)v' ∴ mv=3mv' ⇒ v'=v3