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.

#Mechanics

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Comments

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

Spandan Senapati - 3 years, 5 months ago

how u derived the first formula

Arun Palaniappan - 3 years, 5 months ago

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

Spandan Senapati - 3 years, 5 months ago

@Spandan Senapati – your answer is dimensionally incorrect it would be better if u correct it

omswostik mishra - 3 years, 5 months ago

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

Spandan Senapati - 3 years, 5 months ago

2pi_/(3m/8k)

Arunava Das - 3 years, 5 months ago

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Jamie Henry - 1 year, 9 months ago

π(m/k)^(1/2)

Ankitesh kumar - 3 years, 5 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$