A stone of mass 1 kg is tied to end of a massless string of length 1 m. If the breaking tension of the string is 400 N, then maximum linear velocity, the stone can have without breaking the string, while rotating in horizontal plane, is:

A stone of mass 1 kg tied to a string of length 1 m is rotated in a horizontal plane. The breaking tension is 400 N. We need the maximum linear velocity.

We start by noting that

For circular motion in a horizontal plane, the tension in the string provides the centripetal force needed to keep the stone moving in a circle:

$$ T = \frac{mv^2}{r} $$

where $$m$$ is the mass, $$v$$ is the linear velocity, and $$r$$ is the radius of the circle (equal to the string length).

Next,

The string breaks when $$T > 400$$ N. For the maximum velocity without breaking:

$$ T_{\max} = \frac{mv_{\max}^2}{r} $$

$$ v_{\max} = \sqrt{\frac{T_{\max} \times r}{m}} = \sqrt{\frac{400 \times 1}{1}} = \sqrt{400} = 20\;\text{m/s} $$

The maximum linear velocity is 20 m s$$^{-1}$$.

The correct answer is Option 1: 20 m s$$^{-1}$$.