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 Ff and Fw are the reaction forces of the floor and the wall, then ratio of Fw/Ff will be:
(Use g = 10 m/s2)

Fig.

• A. $\frac{6}{\sqrt{110}}$
• B. $\frac{3}{\sqrt{113}}$
• C. $\frac{3}{\sqrt{109}}$
• D. $\frac{2}{\sqrt{109}}$

Answer 1

Answer: (C)

$\frac{3}{\sqrt{109}}$

Answer 2

The correct answer is (C) : $\frac{3}{\sqrt{109}}$

Fig.

Taking torque from B
$F_w×5=\frac{3}{2}mg$
$⇒F_w=\frac{3}{10}×10×10$
= 30 N
N = mg = 100 N
and fr = Fw = 30 N
so
$F_f=\sqrt{N^2+f_{r}^{2}}=\sqrt{10900}=10\sqrt{109}$ N
therefore ,
$\frac{F_w}{F_f}=\frac{3}{\sqrt{109}}$