Question

A $\sqrt{34}$ m long ladder weighing 10kg leans on a frictionless wall. Its feet rest on the floor 3m 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 $\frac{F_w}{F_f}$ will be: (Use g = 10 m/s2)

• 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

Taking torque from B
$Fw\times5= \frac{3}{2} \text{ mg}$
$\Rightarrow Fw= \frac{3}{10} \times 10 \times 10 = 30 N$

N = mg = 100 N
and fr = Fw = 30 N

So, Ef=$\sqrt{N_2+f_r2}$
Ef = $\sqrt{10900}$
Ef = 10$\sqrt{109}$

$\frac{F_r}{F_w}$=$\frac{3}{\sqrt{109}}$