Question

What is centripetal force?Derive an expression for it.show that centripetal force does no work.

Answer 1

According to Newton’s first law of motion, a body possesses the
property called directional inertia (i.e) the inability of the body to change
its direction. This means that without the
application of an external force, the direction
of motion can not be changed. Thus when
a body is moving along a circular path,
some force must be acting upon it, which
continuously changes the body from its
straight-line path. It makes clear
that the applied force should have no
component in the direction of the motion of
the body or the force must act at every point perpendicular to the direction of motion of the body. This force,
therefore, must act along the radius and should be directed towards the
centre.
Hence for circular motion, a constant force should act on the body,
along the radius towards the centre and perpendicular to the velocity
of the body. This force is known as centripetal force.
If m is the mass of the body, then the magnitude of the centripetal
force is given by
F = mass × centripetal acceleration
= m (v²/r)=mv²/r=mrw²

Examples:
Any force like gravitational force, frictional force, electric force,
magnetic force etc. may act as a centripetal force. Some of the examples
of centripetal force are :
(i) In the case of a stone tied to the end of a string whirled in a
circular path, the centripetal force is provided by the tension in the
string.
(ii) When a car takes a turn on the road, the frictional force
between the tyres and the road provides the centripetal force.
(iii) In the case of planets revolving round the Sun or the moon
revolving round the earth, the centripetal force is provided by the
gravitational force of attraction between them
(iv) For an electron revolving round the nucleus in a circular
path, the electrostatic force of attraction between the electron and the
nucleus provides the necessary centripetal force.