A ladder rests against a frictionless vertical wall, with its upper end $6\,m$ above the ground and the lower end $4\,m$ away from the wall. The weight of the ladder is $500 \,N$ and its C. G. at $1/3^{rd}$ distance from the lower end. Wall's reaction will be, (in Newton)
A ladder rests against a frictionless vertical wall, with its upper end $6\,m$ above the ground and the lower end $4\,m$ away from the wall. The weight of the ladder is $500 \,N$ and its C. G. at $1/3^{rd}$ distance from the lower end. Wall's reaction will be, (in Newton)
$111$
$333$
$222$
$129$
A ladder rests against a frictionless vertical wall, with its upper end $6\,m$ above the ground and the lower end $4\,m$ away from the wall. The weight of the ladder is $500 \,N$ and its C. G. at $1/3^{rd}$ distance from the lower end. Wall's reaction will be, (in Newton)
Let the length of the rod is $3 a$, by geometry we have $3 a=\sqrt{(4)^{2}+(6)^{2}}=\sqrt{5^{2}}$
$\uparrow: N_{1}=500$
$\rightarrow: f=N_{2}$
$\tau_{A}=0 \Rightarrow N_{2}(6)=500(a \cos \theta)$
$N_{2}=\frac{500}{6} \times \frac{\sqrt{52}}{3} \times \frac{4}{\sqrt{52}}$
$=\frac{2000}{18}=\frac{1000}{9}=111 N$