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

Answer: (C)

He may have been moving a little over two times as fast

The centripetal acceleration of the skater moving at speed $v$ in initially is given by $\frac{v^2}{R}$.

The new acceleration is five times larger.

$⟹\frac{v^{\prime 2}}{R^{\prime }}=5\frac{v^2}{R}$

Hence if $v^{\prime }=v$, the new radius is one-fifth of the original radius.

If $R=R^{\prime }$,

the new speed is $\sqrt{5}\approx 2.23$ times of original.

Hence correct answer is option C.