Question

A skater moves over ice in a circular path at a constant speed. He later moves over ice in a circular path at a constant speed, but this time with five times as much acceleration as before.
What single difference in the motion of the skater might have caused his acceleration to five times as great?
A- He may have been moving five times as fast as before
B- He may have been moving around a curve with five times the radius of the original circular path
C- He may have been moving a little over two times as fast
D- He may have been moving around a curve with a radius just over twice as much as the original radius.
E- he may have been wearing more massive skates.

Answer 1

Hint: When a body moves in a circular motion it has two types of velocity one is linear velocity while the other is angular velocity. Here the body is moving with constant speed, the magnitude of the speed Also, there are two types of acceleration, one is linear while the other is angular.

Complete step by step answer:
We know centripetal acceleration is given by \[\dfrac{{{v}^{2}}}{r}\], where v is the linear velocity and r is the radius of the circular path.
Now, the acceleration becomes 5 times,
\[\Rightarrow \dfrac{5{{v}^{2}}}{r}\]
\[\therefore \]the new radius is one fifth of the initial one. But, if \[r=r'\]
The new speed is therefore, \[\sqrt{5}\sim2.23\]times the initial one.

So, the correct answer is “Option C”.

Note:
The force which pulls the body towards the centre is centripetal force and the acceleration is called centripetal acceleration. Since, the acceleration increased, either the speed gets increased or the radius gets decreased. There is no role of mass when it comes to speed and acceleration. The equation shows acceleration is independent of the mass.