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Two light strings of length 4 cm and 3 cm are tied to a bob of weight 500 gm. The free ends of the strings are tied to pegs in the same horizontal line and separated by 5 cm. The ratio of tension in the longer string to that in the shorter string is

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5 : 4

3 : 4

4 : 5

4 : 3

answer is B.

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Detailed Solution

$According to Lamie' s theorem$

$\frac{T_{1}}{\sin (90 + θ_{2})} = \frac{T_{2}}{\sin (90 + θ_{1})} = \frac{0.5 g}{\sin 90^{0}}$

$\sin (90 + θ_{2}) = \cos θ_{2} = \frac{3}{5}$

$\sin (90 + θ_{1}) = \cos θ_{1} = \frac{4}{5}$

$\frac{T_{1}}{T_{2}} = \frac{\cos θ_{2}}{\cos θ_{1}} = \frac{3}{4}$

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