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QJEEM22Phfc49: JEE Main 2022 Physics - Class 11 JEEM22Phfc49 Solution: A m long ladder weighing 10 kg leans on a frictionless wall.…

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/s².)

JEE Main 2022 (Online) 28th June Evening Shift Physics - Rotational Motion Question 78 English

Multiple Choice Options

A ${6 \over {\sqrt {110} }}$
B ${3 \over {\sqrt {113} }}$
C ${3 \over {\sqrt {109} }}$
D ${2 \over {\sqrt {109} }}$

Step-by-Step Verified Solution

JEE Main 2022 (Online) 28th June Evening Shift Physics - Rotational Motion Question 78 English Explanation

Taking torque from B

${F_w} \times 5 = {3 \over 2}mg$

$\Rightarrow {F_w} = {3 \over {10}} \times 10 \times 10$

$= 30\,N$

$N = mg = 100\,N$

and ${f_r} = {F_w} = 30\,N$

so ${F_f} = \sqrt {{N^2} + f_r^2} = \sqrt {10900} = 10\sqrt {109} \,N$

so ${{{F_w}} \over {{F_f}}} = {3 \over {\sqrt {109} }}$

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