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(A) The particle moves in a horizontal circle on a smooth table. The forces acting on the particle are:$1$. The gravitational force $(mg)$ acting down

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$T$

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(A) The particle moves in a horizontal circle on a smooth table. The forces acting on the particle are:$1$. The gravitational force $(mg)$ acting downwards.$2$. The normal reaction $(N)$ from the table acting upwards.$3$. The tension $(T)$ in the string acting towards the centre of the circular path.Since the particle is moving in a horizontal circle,there is no vertical acceleration,so $N = mg$.The horizontal force acting towards the centre is the tension $T$,which provides the necessary centripetal force for the circular motion. Therefore,the net force on the particle directed towards the centre is equal to $T$.

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

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