A uniform round object of mass `M`, radius `R` and moment of inertia about its centre of mass `I_(cm)` has a light, thin string wrapped several times around its circumference. The free end of string is attaced to the celling and the object is released from rest. Find the acceleration of centre of the object and tension n the string. [ Take `(I_(cm))/(MR^(2))=k`]

Explanation

When the clock keeps the correct time, it completes one revolutions in 60 5. So the number of revolutions made per second is 1/60 rps.
i.e., `n_(0) = 1//60 rps = 0.017` rps
Final frequency `=n=50/(60 xx 60) = 0.014` rps
Time t = 7 minutes `=7 xx 60 = 420` s
Acceleration `alpha = ?, omega = omega_(0) = omega_(0) + alpha t`
`alpha = (omega - omega_(0))/t = (2pi n - 2pi n_(0))/t = (2pi (0.014 - 0.017))/420`
`=-4.48 xx 10^(-5) rad//s^(2)`