First slide

Mechanical equilibrium force cases

Question

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

Moderate

A

4:3
B

3:4
C

4:5
D

5:4

Solution

Since 3² + 4² = 5^2,The angle between the strings must be 90⁰, as shown in the figure.
$\large \therefore$ cosθ₁ = 4/5, cosθ₂ = 3/5
By Lami's Theorem,
$\fn_phv \large F = \frac{{{T_{1}}}}{{\sin ({{90}^0} + {\theta _1})}} = \frac{{{T_2}}}{{\sin ({{90}^0} + {\theta _2})}} = \frac{W}{{\sin {{90}^0}}}$
$\large \therefore \frac{{{T_2}}}{{{T_1}}} = \frac{{\cos {\theta _2}}}{{\cos {\theta _1}}} = \frac{{3/5}}{{4/5}} = \frac{3}{4}$

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