A cord can bear a maximum force of 100 N without breaking. A body of mass 1 kg tied to one end of a cord of length 1 m is revolved in a horizontal plane. What is the maximum linear speed of the body so that the cord does not break

The correct option is 10 m/s.

Understanding the Physical Principles:
When a body is revolved in a horizontal circle, the tension in the cord provides the necessary centripetal force to keep the body in circular motion. The cord will break if the tension required to maintain this circular path exceeds the maximum force the cord can withstand.

Given Data:
Maximum tension force the cord can bear:
$T_{\text{max}}=100\text{N}$
Mass of the body:
$m=1\text{kg}$
Radius of the horizontal circle (length of the cord):
$r=1\text{m}$

Mathematical Derivation:
The centripetal force required to keep a body in a circular path of radius $r$ at a linear speed $v$ is given by the formula:
$F=\frac{m{v}^2}{r}$
Since the tension in the cord provides this centripetal force, we have:
$T=\frac{m{v}^2}{r}$

To find the maximum linear speed ($v_{\text{max}}$) without breaking the cord, we set the tension to its maximum limit:
$T_{\text{max}}=\frac{m{v}_{\text{max}}^2}{r}$

Now, substitute the given values into the formula:
$100=\frac{1\times v_{\text{max}}^2}{1}$

Solving for $v_{\text{max}}^2$ gives:
$v_{\text{max}}^2=100$

Taking the square root on both sides:
$v_{\text{max}}=\sqrt{100}=10\text{m/s}$

Therefore, the maximum linear speed at which the body can be revolved without breaking the cord is 10 m/s.