Question 153: Centre of Mass and Rotational Motion

Question

A $\sqrt {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 E
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
.)
![](https://app-content.cdn.examgoal.net/fly/@width/image/1l57a2wg6/0056aa6e-515f-4490-84d1-ca683af2fcd1/9b5fd660-fbe3-11ec-9cb0-2b7fdcfae982/file-1l57a2wg7.png?format=png)

Accepted Answer

Taking torque from B
${F_w} 	imes 5 = {3 \over 2}mg$
$ \Rightarrow {F_w} = {3 \over {10}} 	imes 10 	imes 10$
$ = 30\,N$
$N = mg = 100\,N$
and ${f_r} = {F_w} = 30\,N$
so ${F_f} = \sqrt {{N^2} + f_r^2}  = \sqrt {10900}  = 10\sqrt {109} \,N$
so ${{{F_w}} \over {{F_f}}} = {3 \over {\sqrt {109} }}$
![](https://app-content.cdn.examgoal.net/fly/@width/image/1l5hwefzs/f8b080d4-5c58-4a1b-90b2-07807d04ebb3/bbb612d0-01ba-11ed-85a8-43d162d2b7e8/file-1l5hwefzx.png?format=png)

Answer

${6 \over {\sqrt {110} }}$

Answer

${3 \over {\sqrt {113} }}$

Answer

${3 \over {\sqrt {109} }}$

Answer

${2 \over {\sqrt {109} }}$

Centre of Mass and Rotational Motion

A \sqrt {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 E 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 .)

Choose the correct answer: