Question

The blocks B and C in the figure have mass m each. The strings AB and BC are light, having tensions $T_{1}and{T}_2$ respectively. The system is in equilibrium with a constant horizontal force mg acting on C. Then

• A. $tan{\theta }_1=\frac{1}{2}$
• B. $tan{\theta }_2=1$
• C. $T_1=\sqrt{5}mg$
• D. $T_2=\sqrt{2}mg$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A $tan{\theta }_1=\frac{1}{2}$
B $tan{\theta }_2=1$
C $T_1=\sqrt{5}mg$
D $T_2=\sqrt{2}mg$

$T_{2}sin{\theta }_2=mg$ . . . . (i)
$T_{2}cos{\theta }_2=mg\therefore tan{\theta }_1=1$
Again,
$T_{1}sin{\theta }_1=T_{2}sin{\theta }_2$
$T_{1}sin{\theta }_1=mg$ From (i)
$And{T}_{1}cos{\theta }_1=T_{2}cos{\theta }_2+mg\therefore T_{1}cos{\theta }_1=2mg\therefore tan{\theta }_1=\frac{1}{2}$
i.e., $T_2=\sqrt{2}mgand{T}_1=\sqrt{5}mg$