Question

One end of a stick with mass m and length $\ell$ is pivoted on a wall and the other end rest on a frictionless floor, as shown in figure. Let $F_{L}and{F}_R$ be the vertical forces on the left and right ends of the sticks, respectively.Then:-

• A. $F_L=mg/2$
• B. $F_L<F_R$
• C. $F_L=F_R$
• D. $F_L=F=mgcos\theta$

Answer 1

The correct option is C $F_L=F_R$

Ref. image I

For equilibrium $\sum$ moment about pivot $=0$

Ref. image II

$\Rightarrow F_L\times l\cos \theta =mg\times \frac{l}{2}\cos \theta$

$\Rightarrow F_L=\frac{mg}{2}$

$\sum$ Force vertical direction $=0$

$\Rightarrow F_L+F_R=mg$

$\Rightarrow F_R=\frac{mg}{2}$

$\Rightarrow F_L=F_R=\frac{mg}{2}$