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:

Question

A stone of mass 1 kg is tied to end of a massless string of length 1 &#160; m . If the breaking tension of the string is 400 &#160; N , then maximum linear velocity, the stone can have without breaking the string, while rotating in horizontal plane, is:

Aicharya · Accepted Answer

In horizontal circle, tension towards the centre of the circular path at any moment will provide the required centripetal force.

Therefore,

$T_{m a x} = \frac{m v^{2}}{r} \Rightarrow 400 = \frac{1 \times v^{2}}{1} \Rightarrow v = 20 m s^{- 1}$

Alternative Solution: 1. Key Concepts: The problem is based on the concept of circular motion, specifically the centripetal force. Centripetal force is the force that makes a body follow a curved path. In this case, the tension in the string provides the centripetal force required for the stone's circular motion. The stone will break the string if the required centripetal force exceeds the maximum tension that the string can withstand. 2. Step-by-step Solution: The centripetal force, $F_c$, required for circular motion is given by the formula: $F_c=m \cdot v^2 / r$, where: - $m$ is the mass of the object (1 kg in this case), - $v$ is the speed of the object, - $r$ is the radius of the circle (1 m in this case). The maximum tension that the string can withstand is given as 400 N. This means that the maximum centripetal force that can be applied without breaking the string is also 400 N. Therefore, we can set $F_c$ equal to the maximum tension to find the maximum speed $v$: $400 N = 1 kg \cdot v^2 / 1 m$ Solving this equation for $v$ gives: $v = \sqrt{400 N \cdot 1 m / 1 kg} = 20 m/s$. So, the maximum linear velocity the stone can have without breaking the string is 20 m/s. Therefore, the correct answer is A) $20 m/s$. Options B) $40 m/s$, C) $400 m/s$, and D) $10 m/s$ are incorrect because they do not fit the calculation. 3. Tips to Remember this Concept: - The centripetal force required for an object to move in a circular path is proportional to the square of its speed. Hence, if the speed of the object increases, the required centripetal force will increase exponentially. - When an object is moving in a circle, the tension in the string provides the required centripetal force. If the required centripetal force is more than the tension that the string can withstand, the string will break. - In such problems, always equate the maximum tension in the string to the centripetal force to find the maximum speed of the object.

A stone of mass 1 kg is tied to end of a massless string of length 1 &#160; m . If the breaking tension of…

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A stone of mass 1 kg is tied to end of a massless string of length 1 m . If the breaking tension of…