One end of the string of length $l$ is connected to a particle of mass $m$ and the other end is connected to a

Question

One end of the string of length $l$ is connected to a particle of mass $m$ and the other end is connected to a small peg on a smooth horizontal table. If the particle moves in a circle with speed $v$, the net force on the particle (directed towards the centre) will be: ($T$ represents the tension in the string)

Accepted Answer

1. **Identify Forces:** Consider the forces acting on the particle. In the vertical direction, the weight ($mg$) is balanced by the normal reaction ($N$) from the table. In the horizontal plane, the only force acting on the particle is the tension ($T$) exerted by the string directed towards the peg (centre).
2. **Net Force:** According to Newton's Second Law, the net force ($F_{net}$) acting on an object is the vector sum of all individual physical forces acting on it. Here, $F_{net} = T$.
3. **Centripetal Force Concept:** The term $\frac{mv^2}{l}$ represents the mass times the centripetal acceleration ($ma_c$). It is not an independent force of nature but the *result* of the net force. The equation of motion is $T = \frac{mv^2}{l}$.
4. **Conclusion:** The question asks for the net force, which is provided solely by the tension. Thus, the net force is $T$.

(Reference: NCERT Class 11, Physics Part I, Chapter 4: Laws of Motion, Exercise 4.4).

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