A square lamina OABC of side length 10 cm is | vedclass

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(A) For the lamina to be in rotational equilibrium about the pivot point $O$,the net torque $	au_{net}$ about $O$ must be zero.Let the side length be

Vedclass · Accepted Answer

$20 \ N$

Vedclass · Answer

(A) For the lamina to be in rotational equilibrium about the pivot point $O$,the net torque $	au_{net}$ about $O$ must be zero.Let the side length be $\ell = 10 \ cm$.The forces acting on the lamina are:$1$. At corner $C$: $A$ force $F$ acting horizontally to the left (produces counter-clockwise torque $	au_1 = F \cdot \ell$) and a force $10 \ N$ acting vertically upwards (produces counter-clockwise torque $	au_2 = 10 \cdot \ell$).$2$. At corner $B$: $A$ force $10 \ N$ acting vertically upwards (produces clockwise torque $	au_3 = 10 \cdot \ell$) and a force $10 \ N$ acting horizontally to the right (produces clockwise torque $	au_4 = 10 \cdot \ell$).$3$. At corner $A$: $A$ force $10 \ N$ acting horizontally to the right (produces clockwise torque $	au_5 = 10 \cdot \ell$) and a force $10 \ N$ acting vertically downwards (produces clockwise torque $	au_6 = 10 \cdot \ell$).Taking counter-clockwise torque as positive:$	au_{net} = (F \cdot \ell) + (10 \cdot \ell) - (10 \cdot \ell) - (10 \cdot \ell) - (10 \cdot \ell) - (10 \cdot \ell) = 0$$F \cdot \ell + 10 \ell - 40 \ell = 0$$F \cdot \ell = 30 \ell$$F = 30 \ N$.Wait,re-evaluating the torques based on the figure:- Force $F$ at $C$ (distance $\ell$ from $O$): Torque $= F \cdot \ell$ $(CCW)$- Force $10 \ N$ at $C$ (distance $\ell$ from $O$): Torque $= 10 \cdot \ell$ $(CCW)$- Force $10 \ N$ at $B$ (vertical,distance $\ell$ from $O$): Torque $= 10 \cdot \ell$ $(CW)$- Force $10 \ N$ at $B$ (horizontal,distance $\ell$ from $O$): Torque $= 10 \cdot \ell$ $(CW)$- Force $10 \ N$ at $A$ (horizontal,distance $\ell$ from $O$): Torque $= 10 \cdot \ell$ $(CW)$- Force $10 \ N$ at $A$ (vertical,distance $\ell$ from $O$): Torque $= 0$ (line of action passes through $O$)Summing torques: $F \ell + 10 \ell - 10 \ell - 10 \ell - 10 \ell = 0 \Rightarrow F \ell = 20 \ell \Rightarrow F = 20 \ N$.

$A$ square lamina $OABC$ of side length $10 \ cm$ is pivoted at $O$. Forces act on the lamina as shown in the figure. If the lamina remains stationary,then the magnitude of $F$ is:

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