Question

A body of mass 2 kg revolves around a circular path of radius 5 m. If it makes 10
revolutions per second, its centripetal acceleration is
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Answer 1

mass of body(m)= 2 kg

Radius of circle(r)=5 m

rps (revolutions per second)=10 rev / second

As angular velocity (w)= rps (2π)

hence w= 20π radians / second

Centripetal Acceleration(ac)=?

Solution:

ac= v^2/r ……(1)

Bur v=rw put in (1), we get

ac= (r) (w^2)

ac= (5 m) (20π rad/sec)^2

ac= (5 m) (400 π^2 rad^2/sec^2)

ac= 2000 (π^2) rad^2.m/s^2

As s=rθ where θ in radians

θ =S/r = S in meter/ r in meter

radian= meter(m)/ meter(m)

ac= 2000 (π^2) m^2.m/s^2.m^2

ac=2000π^2 m/s^2.

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