The blocks 1 and 2 in the arrangement have mass m each. The strings AB and BC are light, having tension $T_{1} a n d T_{2}$ respectively. The system is in equilibrium with a constant horizontal force mg acting on C. Then

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

$T_{2} = \sqrt{2} m g$

$\tan ϕ_{1} = \frac{1}{2}$

$T_{1} = \sqrt{5} m g$

$\tan ϕ_{2} = 1$

answer is A, B, C, D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

$T_{1} \sin ϕ_{1} = T_{2} \sin ϕ_{2} \to 1$

$T_{1} \cos ϕ_{1} = m g + T_{2} \cos ϕ_{2} \to 2$

$T_{1} \sin ϕ_{2} = m g \to 3$
$T_{2} \cos ϕ_{2} = m g \to 4$

$\frac{3}{4} \Rightarrow \tan φ_{2} = 1$
$φ_{2} = 45^{\circ}$
$\Rightarrow T_{2} \times \frac{1}{\sqrt{2}} = m g \Rightarrow T_{2} = \sqrt{2} m g$
$\begin{array}{l} f r o m (1) T_{1} \sin φ_{1} = m g \\ f r o m (2) T_{1} \cos φ_{1} = 2 m g \end{array}} \Rightarrow \tan φ_{1} = \frac{1}{2}$
$∴ T_{1} = \sqrt{5} m g$