Two blocks are connected with a string and the system is connected to another string which is fixed at the centre of a circular table as shown in the figure. Find the tension in the string which is fixed at the centre.

m ω^{2} r_{1}

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m ω^{2} r_{2}

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m ω^{2} (r_{1} + r_{2})

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m ω^{2} (r_{1} - r_{2})

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Solution

The correct option is C $m ω^{2} (r_{1} + r_{2})$
The free body diagram of the system can be shown as below.

Applying Newton's 2nd law for block 1
$T_{1} - T_{2} = m ω^{2} r_{1} . . . . . . . (i)$
Applying Newton's 2nd law for block 2
$T_{2} = m ω^{2} r_{2} . . . . . . . (i i)$
Adding equation $(i)$ and $(i i)$
$T_{1} = m ω^{2} (r_{1} + r_{2})$

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