Question

Two particles A and B, each of mass m, are kept stationary by applying a horizontal force F= mg on particle B as shown in fig. then

• A.
• B. 2T₁ = 5 T₂
• C.
• D. None of these

Answer 1

The correct option is C

$T_{2}cos\beta =mg;T_{2}sin\beta =mg$

$T_{1}sin\alpha =T_{2}sin\beta =mg\to \left(1\right)T_{1}cos\alpha =mg+T_{2}cos\beta \Rightarrow T_{1}cos\alpha =2mg\to \left(2\right)\frac{\left(1\right)}{\left(2\right)}\Rightarrow tan\alpha =\frac{1}{2}\Rightarrow cos\alpha =\frac{2}{\sqrt{5}}\therefore T_1\frac{2}{\sqrt{5}}=2mg\Rightarrow T_1=mg\sqrt{5}\therefore \frac{T_1}{T_2}=\frac{\sqrt{5}}{\sqrt{2}}\Rightarrow \sqrt{2}{T}_1=\sqrt{5}{T}_2$