Question

In the following figure the masses of the blocks A and B are same and each equal to m. The tensions in the strings OA and AB are $T _ { 2 }$ and $T _ { 1 }$ respectively. The system is in equilibrium with a constant horizontal force mg on B. The $T _ { 1 }$ is

• A. mg
• B. $\sqrt { 2 } m g$
• C. $\sqrt { 3 } \mathrm { mg }$
• D. $\sqrt { 5 } \mathrm { mg }$

Answer 1

Answer: (B)

$\sqrt { 2 } m g$

Answer 2

From the free body diagram of block B

$T _ { 1 } \cos \theta _ { 1 } = m g$……(i)

$T _ { 1 } \sin \theta _ { 1 } = - m g$ …..(ii)

by squaring and adding $T _ { 1 } ^ { 2 } \left( \sin ^ { 2 } \theta _ { 1 } + \cos ^ { 2 } \theta _ { 1 } \right) = 2 ( m g ) ^ { 2 }$

$\therefore$ $T _ { 1 } = \sqrt { 2 } m g$