Q: A block of mass 1/π^{2} 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

**Click to See Answer : **

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