[OCR] 3

Topic: Atomic Structure

A bob of mass 1.5 kg is attached to a string of negligible mass and of length 25.0 cm . The other end of the string is fixed to point $X$ of an inverted " $L$ " structure of arm length $d$. The structure is fixed to the centre of a rotating disc of radius 8.0 cm .\n\nWhen the disc rotates with an angular velocity $\omega$, the string makes at an angle $\theta$ to the vertical as shown in Fig. 3.1.\n\nFig. 3.1 [8.0m]

Part 1: (a) A point on the circumference of the rotating disc has a speed of $24.0 \mathrm{~cm} \mathrm{~s}^{-1}$.\n\nDetermine $\omega$.\n$$\omega=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots$$ [2m]

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Part 2: (b) (i) Determine the tension in the string for $\theta=30^{\circ}$. [2m]

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Part 3: (ii) Calculate $d$.\n$$d=\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots$$ [2m]

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Part 4: (с) A student states that as the angular velocity of the disc increases, $\theta$ increases but $\theta$ will always be smaller than $90^{\circ}$.\n\nComment on the validity of the statement made by the student. [2m]

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