A cricket ball of mass 150 g has an initial velocity u = (3î + 4ĵ) m s⁻¹ and a final velocity v = -(3î + 4ĵ ) m s⁻¹ after being hit. The change in momentum (final momentum-initial momentum) is (in kg m s⁻¹)

The correct option is -(0.9î + 1.2ĵ).

Step-by-step Explanation:

1. Identify the given values:
Mass of the cricket ball, $m=150\text{g}$
First, we must convert the mass from grams to kilograms (kg) to keep the units consistent with the standard SI units ($\text{kg m s}⁻¹$):
$m=\frac{150}{1000}\text{kg}=0.15\text{kg}$

The initial velocity vector is:
$\overrightarrow{u}=(3\mathrm{î}+4\mathrm{ĵ}){\text{m s}}^{-1}$

The final velocity vector is:
$\overrightarrow{v}=-(3\mathrm{î}+4\mathrm{ĵ}){\text{m s}}^{-1}$

2. Formula for Change in Momentum:
The change in momentum ($\Delta \overrightarrow{p}$) is defined as the difference between the final momentum ($\overrightarrow{p_f}$) and the initial momentum ($\overrightarrow{p_i}$):
$\Delta \overrightarrow{p}=\overrightarrow{p_f}-\overrightarrow{p_i}$
Since momentum is the product of mass and velocity ($\overrightarrow{p}=m\overrightarrow{v}$), we can write:
$\Delta \overrightarrow{p}=m\overrightarrow{v}-m\overrightarrow{u}=m(\overrightarrow{v}-\overrightarrow{u})$

3. Calculate the difference in velocity:
$\overrightarrow{v}-\overrightarrow{u}=-(3\mathrm{î}+4\mathrm{ĵ})-(3\mathrm{î}+4\mathrm{ĵ})$
$\overrightarrow{v}-\overrightarrow{u}=-2(3\mathrm{î}+4\mathrm{ĵ})=-(6\mathrm{î}+8\mathrm{ĵ})$

4. Calculate the change in momentum:
Multiply the mass by the change in velocity:
$\Delta \overrightarrow{p}=0.15\times [-(6\mathrm{î}+8\mathrm{ĵ}\left)\right]$
$\Delta \overrightarrow{p}=-(0.15\times 6\mathrm{î}+0.15\times 8\mathrm{ĵ})$
$\Delta \overrightarrow{p}=-(0.9\mathrm{î}+1.2\mathrm{ĵ}){\text{kg m s}}^{-1}$

Thus, the change in momentum of the cricket ball is -(0.9î + 1.2ĵ) kg m s⁻¹.