Question

An object of mass 400 grams is whirled in a horizontal circle of radius 2m. If it performs 60 r.p.m, calculate the centripetal force.

Answer 1

Hint: Any force which forces the body to undergo a uniform circular motion is known as centripetal force. It is a vector quantity. Centripetal force can be produced using one or more than on forces acting on the body.

As per the given data,
The radius of circle 2m
Angular Speed of rotation 60 r.p.m

Formula to be used:
${{F}_{c}}=m{{\omega }^{2}}r$

Complete answer:
Centripetal force makes a body move in a circular path with a uniform velocity. The force is always pointed towards the center of the circle. In classical mechanics, gravity provides a centripetal force for the acceleration of astronomical objects in an orbit.
In consideration of this question where a 400g body undergoes in a circular motion along a virtual horizontal circle of radius 2m. The condition is shown in below diagram,

Angular speed is given as 60r.p.m. So the angular speed on movement per second is given by:
$\begin{align}
  & \omega =\dfrac{60}{1m} \\
 & \Rightarrow \dfrac{60}{60s} \\
 & \Rightarrow \omega =1r.p.s \\
\end{align}$
The value of angular speed (velocity) in radians is given by,
$\omega =2\pi \,rad{{s}^{-1}}$
The angular acceleration of the body can be written as:
\[{{a}_{c}}={{\omega }^{2}}r\]
The centripetal force is dependent on the mass of the body (In kg), the radius with which it is rotating on an axis or point, and the angular acceleration of the body. Mathematically:
$\begin{align}
  & {{F}_{c}}=m{{a}_{c}} \\
 & \Rightarrow {{F}_{c}}=m{{\omega }^{2}}r \\
\end{align}$
By putting the values as her the given and derived data. The centripetal force can be expressed as:
$\begin{align}
  & {{F}_{c}}=0.4\times (4{{\pi }^{2}})\times 2 \\
 & \Rightarrow 3.2{{\pi }^{2}} \\
 & \Rightarrow {{F}_{c}}=31.58N \\
\end{align}$
The value of centripetal force acting on the body which is responsible for the uniform circular motion of the body is $31.58N$.

Note:
Centripetal force always makes a body move in a circular path. It was beautifully explained by Sir Isaac Newton. While calculating the centripetal force the values should be considered in standard form as per the principle of centripetal force or else there will be a calculation error.