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 $v$ the net force on the particle (directed towards the centre) is :
$(i) \;T,$ $(ii)\; T-\frac{m v^{2}}{l},$ $(iii)\;T+\frac{m v^{2}}{l},$ $(iv) \;0$
$T$ is the tension in the string. [Choose the correct alternative].
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 $v$ the net force on the particle (directed towards the centre) is :
$(i) \;T,$ $(ii)\; T-\frac{m v^{2}}{l},$ $(iii)\;T+\frac{m v^{2}}{l},$ $(iv) \;0$
$T$ is the tension in the string. [Choose the correct alternative].
$(i)$ $T$ When a particle connected to a string revolves in a circular path around a centre, the centripetal force is provided by the tension produced in the string. Hence, in the given case, the net force on the particle is the tension $T$, i.e.,
$F=T=\frac{m v^{2}}{l}$
Where $F$ is the net force acting on the particle.
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Give the magnitude and direction of the net force acting on
$(a)$ a drop of rain falling down with a constant speed,
$(b)$ a cork of mass $10\; g$ floating on water,
$(c)$ a kite skillfully held stationary in the sky,
$(d)$ a car moving with a constant velocity of $30\; km/h$ on a rough road,
$(e)$ a high-speed electron in space far from all material objects, and free of electric and magnetic fields.
Give the magnitude and direction of the net force acting on
$(a)$ a drop of rain falling down with a constant speed,
$(b)$ a cork of mass $10\; g$ floating on water,
$(c)$ a kite skillfully held stationary in the sky,
$(d)$ a car moving with a constant velocity of $30\; km/h$ on a rough road,
$(e)$ a high-speed electron in space far from all material objects, and free of electric and magnetic fields.