Question

A uniform rope of length 13 m tied on peg A on a wall passes over frictionless peg B fixed in level with the peg A as shown in figure. In equilibrium, if the length of the rope hanging between pegs is 8 m, then angle $\theta$ [in degrees] which rope makes with wall is (Write upto two digits after the decimal point.)

Answer 1

Balancing the force of the 5m part in the vertical direction,
$T=5mg$ - (1)

Balancing the force of the 8m part in the vertical direction,
$2T\cos \theta =8mg$ - (2)

From (1) and (2),
$2\times 5mg\cos \theta =8mg$
$\cos \theta =\frac{4}{5}\Rightarrow \theta ={37}^{\circ }$