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 $T_2=\sqrt{2}mg$


$T_2\sin {\theta }_2=mg$ ... (1)
$T_2\cos {\theta }_2=mg$ ... (2)
$\therefore \tan {\theta }_2=1$
Again,
$T_1\sin {\theta }_1=T_2\sin {\theta }_2$
$T_1\sin {\theta }_1=mg$ from (1)
and $T_1\cos {\theta }_1=T_2\cos {\theta }_2+mg$
$\therefore T_1\cos {\theta }_1=2mg$
$\therefore \tan {\theta }_1=\frac{1}{2}$
$\therefore T_2=\sqrt{2}mg$ and $T_1=\sqrt{5}mg$