Question

A uniform thin rod of mass $M$ and length $L$ lying in x-y plane is hinged at a fixed support as shown. The rod is free to rotate about fixed axis parallel to z-axis and passing though hinge without friction. At the shown instant the rod is at rest and a force of magnitude $F$ is applied perpendicular to rod at a distance $x$ from hinge. Neglecting gravity, the magnitude of force exerted by hinge on the rod at the shown instant is:

• A. $\left|F(1-\frac{x}{2L})\right|$
• B. $F(1-\frac{3x}{2L})$
• C. $F(1-\frac{2x}{2L})$
• D. $F(1-\frac{4x}{2L})$

Answer 1

The correct option is B $F(1-\frac{3x}{2L})$

As it starts from rest;

centripetal acceleration $=a_c=0$

$\therefore N_x=0$

Now, $F_x=\frac{mL}{3}\propto$ $[\tau .I\propto ]$

$\propto =\frac{3F_x}{\frac{n}{2}}$

Also $a_{cn}.\propto \frac{1}{2}=\frac{3F_x}{2nl}$

and $N_y+F=n{a}_{cn}$

$N_y=n{a}_{cn}-F$

$N_y=\frac{3F_x}{2l}-F$

$N_y=F[\frac{3x}{2l}-1]$

$N_y$ changes direction depending upon the value of $x$.