# Tessellate S.T.E.M.S - Physics - School - Set 1 - Subjective Problem

A pulley in the form of a circular disc of mass $$m$$ and radius $$r$$ has the groove cut all along the perimeter. A string whose one end is attached over to the ceiling passes over this disc pulley and its other end is attached to a spring of spring constant k. The other end of the spring is attached to the ceiling as shown in the figure. Find the time period of vertical oscillations of the centre of mass assuming that the string does not slip over the pulley?

This problem is a part of Tessellate S.T.E.M.S.

Note by Writabrata Bhattacharya
9 months, 4 weeks ago

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$\omega ^2=\frac {4kx}{1+\frac {I_{cm}}{mR^2}}$,therefore here $$\omega =\sqrt \frac {8k}{3m}$$

- 9 months, 2 weeks ago

how u derived the first formula

- 9 months, 2 weeks ago

Refer HC Verma. The question had been directly copied from there

- 9 months, 1 week ago

your answer is dimensionally incorrect it would be better if u correct it

- 9 months, 1 week ago

I am not used to doing such mistakes.Kindly check it correctly the answer is correct as are the dimensions.

- 9 months, 1 week ago

2pi_/(3m/8k)

- 9 months, 1 week ago

π(m/k)^(1/2)

- 9 months, 3 weeks ago