A body of mass 10 kg at rest is acted upon simultaneously by two forces 4N and 3N at right angles to each other. The kinetic energy of the body at the end of 10 sec is

The correct option is 125 J.

Step-by-step derivation:

1. Find the net force acting on the body:
Since the two forces of magnitude 4 N and 3 N act simultaneously at right angles (90°) to each other, their resultant or net force ($F_{\text{net}}$) can be calculated using the Pythagorean theorem:
$F_{\text{net}}=\sqrt{{F_1}^2+{F_2}^2}$
Substituting the given values:
$F_{\text{net}}=\sqrt{4^2+3^2}$
$F_{\text{net}}=\sqrt{16+9}$
$F_{\text{net}}=\sqrt{25}=5\text{N}$

2. Calculate the acceleration of the body:
Using Newton's second law of motion ($F=ma$), where mass $m=10\text{kg}$:
$a=\frac{F_{\text{net}}}{m}$
$a=\frac{5}{10}=0.5{\text{m/s}}^2$

3. Calculate the velocity of the body at the end of 10 seconds:
The body starts from rest, so its initial velocity $u=0$.
Using the first equation of motion:
$v=u+at$
Substituting $t=10\text{s}$ and $a=0.5{\text{m/s}}^2$:
$v=0+(0.5\times 10)$
$v=5\text{m/s}$

4. Calculate the kinetic energy of the body:
The formula for kinetic energy ($\mathrm{K.E.}$) is:
$\mathrm{K.E.}=\frac{1}{2}m{v}^2$
Substituting the values of mass and velocity:
$\mathrm{K.E.}=\frac{1}{2}\times 10\times 5^2$
$\mathrm{K.E.}=5\times 25$
$\mathrm{K.E.}=125\text{J}$