Question

A carpenter's square has the shape of an L as in figure, a force F is applied at distance x, find x for translatory motion of body.

• A. 22 cm
• B. 26 cm
• C. 24 cm
• D. 18 cm

Answer 1

The correct option is C 24 cm

Force must pass through C.M for translational motion.$M_1=\sigma (A{)}_1=\sigma (36\left)\right(3)=\sigma (108)$
$M_2=\sigma A_2=\sigma \left(21\right)\left(3\right)=\sigma \left(63\right)$
$y=\frac{m_1{y}_1+m_2{y}_2}{m_1+m_2}$
$=\frac{\mathrm{\sigma /}\left(108\right)\left(18\right)+\mathrm{\sigma /}\left(63\right)\left(1.5\right)}{\mathrm{\sigma /}(108+\mathrm{\sigma /}(63\left)\right)}$
Force must pass through C.M = 12 cm from lower end
$\Rightarrow$ x= 24 cm