Question

A body of mass 15kg is suspended by two massless string t1 is 60degree t2 is 30 degree angle. Then t1/t2?

Answer 1

By the force balance equation in X direction we can say

$T_1sin60 = T_2sin30$

$\sqrt3 T_1 = T_2$

also in Y direction we can say

$T_1cos60 + T_2cos30 = mg$

$0.5T_1 + 0.866 T_2 = 15*9.8$

now solve above two equations for T1 and T2

$T_1*0.5 + 0.866 *\sqrt3 T_1 = 147$

$2T_1 = 147$

$T_1 = 73.5 N$

also we can find T2 now

$T_2 = \sqrt3 T_1 = 127.3 N$

Now the ratio of T1 and T2 will be

$T_1 : T_2 = 1 :\sqrt3$

so above is the ratio of two tension