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4-1.Newton's Laws of Motion
hard
આપેલ તંત્ર માટે તણાવ ${T_2}$ શું થાય?
A
$mg$
B
$\sqrt 2 \,mg$
C
$\sqrt 3 \,mg$
D
$\sqrt 5 \,mg$
Solution
${T_1}\cos {\theta _1} = mg$……(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 ${T_2} = \sqrt 5 mg$
Standard 11
Physics
