The figure below show four uniform disks that are initially not translating and

Question

The figure below show four uniform disks that are initially not translating and not rotating in outer space. There are no forces on the disks other than the ones shown below. Three forces, of magnitude F, 2F, or 3F, act on each disk; each force is applied either at the rim, at the center, or halfway between rim and center. The force vectors rotate along with the disks, and, in the "snapshots" of the figure below, point either left or right.

A. a only B. b only C. c only D. d only E. a and c F. a and d G. c and d H. a, c, and d

Explanation / Answer

For disk a,

Equilibrium force,

F' =3F-2F -F =0,

Moemt @ centre,

M= 2F(1/2)R -F*R =0

Hence disk a is in quilibrium

For disk b,

Equilibrium force,

F' =3F+2F 1F =6F not equal to zero,

Hence disk b is not quilibrium

For disk c,

Equilibrium force,

F' =2F-F -F =0,

Moemt @ centre,

M= F*R -F*R =0

Hence disk c is in quilibrium

For disk d,

Equilibrium force,

F' =2F-F -F =0,

Momemt @ centre,

M= 2F*R -F*R =F*R

Hence disk d is not in static quilibrium.

G: Disk a and c are in static eqilibrium.

Note: for being in equilibrium, net force and moment at the centre must be zero.

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