Passage
A thin uniform rod of negligible mass and length 0.200 m is attached to the floor by a frictionless hinge at point Pas shown in the figure. A horizontal spring with force contant `k=4.80Nm^(-1)` connects to the other end of the rod to a vertical wall. The rod is in a uniform magnetic field B=0.340 T directed into the plane of the figure. There is current I=6.50 A in the rod, in the direction shown.

When the rod is in equilibrium and makes an angle of `53.0^(@)` with the floor, is the spring stretched or compressed

Options

A. 0.05765 m stretched
B. 0.05765 m compressed
C. 0.0242 m stretched
D. 0.0242 m compressed

Answer

B

Explanation

`F_(1)` produces a clockwise torque, so the spring force must produce a counter clockwise torque. The spring force must be to the left, the spring is stretched.
Find x, the amount the spring is stretched, axis at hinge, counter clockwise torques positive
`(kx)l sin 53^(@)-(1)/(2) Il^(2) B =0, x=(IlB)/(2k sin 53^(@))=((6.50) (0.20) (0.340))/(2xx4.80sin53^(@))=0.05765m`