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A body of mass $5kg$ is revolving along a circle of radius $2m$, with a uniform speed of $4m{s^{ - 1}}$. The centripetal force acting on the body is ______N.
A) $35N$
B) $Zero$
C) $40N$
D) $20N$

Last updated date: 17th Jul 2024
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Hint: In the above question they have asked to find the centripetal force of a body undergoing circular motion. The mass of the body, radius of the body and velocity of the body is given in the question. Apply the given data to find the centripetal force of a body.

Formula used:
$F = \dfrac{{m{v^2}}}{r}$
Where $F$ is the centripetal force, $r$ is the mass of the body, $v$ is the velocity of the body and $r$ is the radius of the body

Complete step by step answer:
Centripetal force is the net force required by a body to perform uniform circular motion. The direction of centripetal force is in the direction of centripetal acceleration; that is it is directed along the radius towards the center.
Data given: Mass of the body \[m = 5{\text{ }}kg\], radius of the body \[r = 2m\] and velocity of the body \[ = 4m/s\]
Centripetal force is given by the formula
$F = \dfrac{{m{v^2}}}{r}$
Now substitute the given data and find its centripetal force
$F = \dfrac{{5 \times {{\left( 4 \right)}^2}}}{2}$
On squaring the value we get,
$F = \dfrac{{5 \times 16}}{2}$
On cancel the term we get,
$F = 5 \times 8$
Let us multiply the terms we get,
$F = 40N$

Therefore option (C) is the correct option.

Additional information: Centripetal acceleration of the body is the acceleration of the body when the body undergoes circular motion. Centripetal acceleration is given by the formula $a = \dfrac{{{v^2}}}{r}$ where $a$ is centripetal acceleration, $v$ is velocity of the body, $r$ is the radius of the body.

Note: Centripetal force causes centripetal acceleration. If centripetal force ceases to act at a point then the body flies off tangentially. Centripetal force comes into picture only when a body is undergoing circular motion. Its direction is towards the center.