A 34 m long ladder weighing 10 kg leans on a frictionless wall. Its feet rest on the floor 3 m away from the wall as shown in the figure. If F f and F w are the reaction forces of the floor and the wa

Question

A 34 m long ladder weighing 10 kg leans on a frictionless wall. Its feet rest on the floor 3 m away from the wall as shown in the figure. If F f and F w are the reaction forces of the floor and the wall, then ratio of F w F f will be : (Use g = 10 m s - 2 .)

TestHub · Accepted Answer

Applying force balance in vertical direction

$N_{1} = m g = 100 N$

Applying torque balance at the bottom contact point,

$m g \times \frac{3}{2} = N_{2} \times 5 \Rightarrow N_{2} = F_{w} = 30 N$

Applying force balance in horizontal direction

$f_{s} = N_{2} = 30 N$

Net reaction at the floor will be,

$F_{f} = \sqrt{{N_{1}}^{2} + {f_{s}}^{2}} = \sqrt{100^{2} + 30^{2}} = 10 \sqrt{109} N$

Therefore, $\frac{F_{w}}{F_{f}} = \frac{30}{10 \sqrt{109}} = \frac{3}{\sqrt{109}}$

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