Two spheres P and Q,each of mass 200 text{ g} | vedclass

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(B) Let $m = 200 	ext{ g} = 0.2 	ext{ kg}$ be the mass of each sphere.Let $L = 1 	ext{ m}$ be the total length of the string.Since $P$ is the mid-p

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$\frac{2}{3}$

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(B) Let $m = 200 	ext{ g} = 0.2 	ext{ kg}$ be the mass of each sphere.Let $L = 1 	ext{ m}$ be the total length of the string.Since $P$ is the mid-point,the distance $OP = 0.5 	ext{ m}$ and $PQ = 0.5 	ext{ m}$.Let $\omega$ be the constant angular speed.$1$. Tension $T_1$ in the string between $P$ and $Q$ provides the centripetal force for sphere $Q$:$T_1 = m \cdot r_Q \cdot \omega^2 = m \cdot L \cdot \omega^2 = 0.2 \cdot 1 \cdot \omega^2 = 0.2 \omega^2$.$2$. Tension $T_2$ in the string between $O$ and $P$ provides the centripetal force for both spheres $P$ and $Q$:$T_2 = m \cdot r_P \cdot \omega^2 + T_1 = m \cdot (0.5) \cdot \omega^2 + 0.2 \omega^2 = 0.2 \cdot 0.5 \cdot \omega^2 + 0.2 \omega^2 = 0.1 \omega^2 + 0.2 \omega^2 = 0.3 \omega^2$.$3$. The ratio of the tension between $P$ and $Q$ to that between $P$ and $O$ is:$\frac{T_1}{T_2} = \frac{0.2 \omega^2}{0.3 \omega^2} = \frac{2}{3}$.

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