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Average Rate of Change

Two particles...

Question

Two particles each of mass $m$ are moving in the horizontal circle with same angular speed. If both the strings are of same length then the ratio of tension is string $\frac{T_{1}}{T_{2}}$ is:

\frac{3}{2}

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3

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2

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\frac{1}{3}

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Solution

The correct option is A $\frac{3}{2}$
Correct option is A

$t_{2} = m (2 l) w^{2} - - - - - - - - - - - (1)$

$t_{1} - t_{2} = m l w^{2} - - - - - - - - - - - - (2)$

Ratio of both equation (1)&(2)

$\frac{t_{1} - t_{2}}{t_{2}} = \frac{1}{2}$

$2 (t_{1} - t_{2}) = t_{2}$

$2 t_{1} - 2 t_{2} = t_{2}$

$2 t_{1} = t_{2} + 2 t_{2}$

$2 t_{1} = 3 t_{2}$

$\frac{t_{1}}{t_{2}} = \frac{3}{2}$

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