4.1 , newtons laws of motion — Physics STD 11 Science — Question

${T_1}\sin {\theta _1} = - mg$…..(ii)

$T_1^2\left( {{{\sin }^2}{\theta _1} + {{\cos }^2}{\theta _1}} \right) = 2{\left( {mg} \right)^2}$

$\therefore $ ${T_1} = \sqrt 2 mg$

${T_2}\cos {\theta _2} = mg + {T_1}\cos {\theta _1}$

${T_2}\cos {\theta _2} = mg + \sqrt 2 mg\,\cos 45^\circ $

${T_2}\cos {\theta _2} = 2mg$…..(i)

${T_2}\sin {\theta _2} = {T_1}\sin {\theta _1}$

$ = \sqrt 2 mg\,\sin 45^\circ $

${T_2}\sin {\theta _2} = mg$…..(ii)

$T_2^2 = 5{(mg)^2}$ or ${T_2} = \sqrt 5 mg$