Q: A block of mass 1/π2 kg is constrained to move in a circular path and makes one revolution in 1 s . It is attached to the centre of circle by a light spring of spring constant 5 N/m and natural length 1 m. the radius of the circular path is
(a) 1 m
(b) 1.1 m
(c) 3 m
(d) 5 m
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Ans: (d)
Sol: k = 5 N/m , ω = 2 π ×1 = 2 π
Let r = radius of circular path
$\displaystyle k x = m \omega^2 r$
$\displaystyle k (r – 1) = m \omega^2 r$
$\displaystyle k r – k = m \omega^2 r$
$\displaystyle k r – m \omega^2 r = k $
$\displaystyle r (k – m \omega^2 ) = k $
$\displaystyle r = \frac{k}{(k – m \omega^2 )} $
$\displaystyle r = \frac{5}{(5 – (\frac{1}{\pi^2}) (2 \pi)^2 )} $
r = 5 m