Question

A $2\text{kg}$ ball moving straight down strikes the floor at $8{\text{ms}}^{-1}$. It rebounds upwards at $6{\text{ms}}^{-1}$. The change in the magnitude of momentum:

• A. $28{\text{kg‐ms}}^{-1}$
• B. $4{\text{kg‐ms}}^{-1}$
• C. $2{\text{kg‐ms}}^{-1}$
• D. $14{\text{kg‐ms}}^{-1}$

Answer 1

The correct option is B

$4{\text{kg‐ms}}^{-1}$

Step 1: Concept of momentum

Change in the magnitude of momentum = magnitude of final momentum – the magnitude of initial momentum.

$∆P=P_f-P_i$, where $P_i$is the initial momentum and $P_f$ is the final momentum.

The magnitude of momentum is calculated using the formula,$P=m\times v$ ; where m = mass of the object and v = velocity of the object.

Initial momentum, $P_i=m\times v_i$; where $v_i$ is the initial velocity

Final momentum, $P_f=m\times v_f$; where $v_f$ is the final velocity

Step 2: Given data and calculation of change in momentum

Given:

Mass of the ball , $m=2\text{kg}$.

Initial velocity, $v_i=8{\text{ms}}^{-1}$.

Final velocity, $v_f=6{\text{ms}}^{-1}$

The magnitude of initial momentum,

$\begin{array}{rcl}{P}_i& =& m\times v_i\\ & =& 2\times 8\\ & =& 16{\text{kg‐ms}}^{-1}\end{array}$

The magnitude of final momentum,

$\begin{array}{rcl}{P}_f& =& m\times v_f\\ & =& 2\times 6\\ & =& 12{\text{kg‐ms}}^{-1}\end{array}$

So,

$\begin{array}{rcl}∆P& =& P_f-P_i\\ & =& 12-16\\ & =& -4{\text{kg‐ms}}^{-1}\end{array}$

Thus, the change in magnitude of momentum = $4{\text{kg‐ms}}^{-1}$(negative sign can be omitted as we are mentioning only the change)

Hence, option (b) is correct.