A 300 g mass has a velocity of (3î + 4ĵ) m/sec at a certain instant. What is its kinetic energy

To find the kinetic energy of the mass, we can use the standard physics formula for kinetic energy:

$K=\frac{1}{2}m{v}^2$

where:
- $m$ is the mass of the object in kilograms (kg)
- $v$ is the speed (magnitude of the velocity vector) in meters per second (m/s)

Step 1: Convert the mass to SI units (kilograms)
The given mass is $300\text{g}$. Since $1\text{kg}=1000\text{g}$:
$m=\frac{300}{1000}\text{kg}=0.3\text{kg}$

Step 2: Calculate the magnitude of the velocity vector (speed)
The velocity vector is given as $\overrightarrow{v}=(3\hat{i}+4\hat{j})\text{m/s}$.
The square of the speed, $v^2$, is the dot product of the velocity vector with itself:
$v^2={\left(v_x\right)}^2+{\left(v_y\right)}^2$
$v^2=3^2+4^2=9+16=25{\text{m}}^2/{\text{s}}^2$

Step 3: Calculate the kinetic energy
Substitute the values of $m$ and $v^2$ into the kinetic energy formula:
$K=\frac{1}{2}\times 0.3\text{kg}\times 25{\text{m}}^2/{\text{s}}^2$
$K=0.15\times 25\text{J}$
$K=3.75\text{J}$

Therefore, the correct option is 3.75 J.