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  • As shown in diagram a ladder of mass M and length l is palced in equilibrium against a smooth vertical wall and a rough horizontal surface . If <img alt="\theta" src="https://learn.careers360.

As shown in diagram a ladder of mass M and length l is palced in equilibrium against a smooth vertical wall and a rough horizontal surface . If \theta be the angle of inclination of the rod with horizoantal then what is the normal reaction of wall on the ladder 

Option: 1

\frac{1}{2} mg \cot \theta


Option: 2

\frac{1}{2} mg \tan \theta


Option: 3

mg \cos \theta


Option: 4

\frac{1}{2} mg


Answers (1)

As we have learned

Equilibrium -

\sum \vec{F}=0  means  Translational equilibrium

 

\sum \vec{\tau }=0     means Rotational equilibrium

-

 

Draw FBD

condition of translational equilibrium 

\sum F_x = 0 \Rightarrow F_r - N = 0 \\ F_r = N ....(1)\\\\ Similarly \ \sum F_y = 0 \: \: \: \\ \ N _1-mg = 0 \\\\ N_1 = mg ....(2)

Taking torque about center of rod

and using  \sum \tau _c=0

from (1) and (2) 

N_1 \frac{l}{2}\cos \theta - f_r\frac{l}{2}\sin \theta-N\frac{l}{2} \sin \theta = 0 \\\\

mg \frac{l}{2}\cos \theta - Nl \sin \theta = 0 \\\\ N = \frac{mg }{2 \tan \theta } = \frac{1}{2} mg \cot \theta

 

 

 

 

 

Posted by

Ramraj Saini

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