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Two balls of mass \mathrm{m_1}=1.0 \mathrm{~kg} and m_2=0.5 \mathrm{~kg} are suspended on two strings of length l_1=10 \mathrm{~cm} and l_2=20 \mathrm{~cm} at the end of a freely hanging rod.

The rod is rotating with an angular velocity of 15 \mathrm{rad} / \mathrm{s} about the vertical axle such that it remains in the vertical position. If the tension in the strings are T_1 and T_2 respectively, then find the sum of T_1 and T_2.

Option: 1

22.5 N


Option: 2

45.0 N


Option: 3

3.0 N


Option: 4

1.5 N


Answers (1)

best_answer

As there is no vertical motion involved,

    \begin{aligned} & T_1 \cos \alpha=m_1 g \\ & T_2 \cos \beta=m_2 g \\ & T_1 \sin \alpha=m_1 \omega^2 l_1 \sin \alpha \\ & T_1=m_1 \omega^2 l_1 \\ & T_2 \sin \beta=m_2 \omega^2 l_2 \sin \beta \\ & T_2=m_2 \omega^2 l_2 \\ & T_1+T_2=\omega^2\left(m_1 l_1+m_2 l_2\right) \\ & =(15)^2[ 1.0 \times 0.1+0.5 \times 0.2] \\ & =(22.5)(0.1+0.1) \\ & =225 \times 0.2 \\ & =45 \mathrm{~N} \\ & \end{aligned}

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