First, let's analyze the given information. The radius of the circular path,
r, is given as
‌ meters. The frequency of revolution,
f, is numerically equal to the radius, so
f=r=‌‌Hz.
The acceleration we need to find is the centripetal acceleration, which is given by the formula:
a=ω2rHere,
ω (omega) is the angular velocity, which can be calculated from the frequency
f using the relationship:
ω=2πf Substitute
f=‌ into the equation for
ω :
ω=2π(‌)=10‌rad∕ sNow, substitute
ω=10‌rad∕ s and
r=‌ meters into the centripetal acceleration formula:
a=ω2r=(10)2(‌) Thus, the acceleration
a is:
a=100(‌)=‌m∕ s2Therefore, the correct option is:
Option D:
(‌)ms−2