MCQ
For given systen $T_2$ .......
- A$mg$
- B$\sqrt 2 \,mg$
- C$\sqrt 3 \,mg$
- ✓$\sqrt 5 \,mg$
✓
Answer
Correct option: D.
$\sqrt 5 \,mg$
d
${T_1}\cos {\theta _1} = mg$……(i)
${T_1}\cos {\theta _1} = mg$……(i)
${T_1}\sin {\theta _1} = - mg$…..(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 ${T_2} = \sqrt 5 mg$
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