2. A hanged ball moves in a horizontal circle, as shown in the figure below. The length of the string is L, and the gravitational acceleration is g. What is the period of this circular motion? (A)\( 2\pi\sqrt{\frac{L\cos\theta}{g}} \) (B)\( \sqrt{\frac{L\cos\theta}{g}} \) (C)\( \frac{1}{2\pi}\sqrt{\frac{L\cos\theta}{g}} \) (D)\( 2\pi\sqrt{\frac{L}{g}}\cos\theta \) (E)\( \frac{1}{2\pi}\sqrt{\frac{L}{g}}\cos\theta \)

6. A small disk of radius \( R_1 \) is fastened coaxially to a larger disk of radius \( R_2 \). The combination is free to rotate on a fixed axle, which is perpendicular to a horizontal frictionless table top, as shown in the overhead view below. The rotational inertia of the combination is I. A string is wrapped around the larger disk and attached to a block of mass m, on the table. Another string is wrapped around the smaller disk and is pulled with a force \( \overrightarrow{F} \) as shown in fig. below. The tension in the string pulling the block is: (A)\( \frac{mR_1F}{R_2} \) (B)\( \frac{mR_1R_2F}{I - mR_2^2} \) (C)\( \frac{mR_1R_2F}{I + mR_2^2} \) (D)\( \frac{mR_1R_2F}{I - mR_1R_2} \) (E)\( \frac{mR_1R_2F}{I + mR_1R_2} \)

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