Q. Equal torsional torques act on two rods $x\ and\ y$ having equal length. The diameter of rod y is twice the diameter of rod $x.If\ \theta_{x}\ and\ \theta_{y}$ are the angles of twist, then $\frac{\theta_{x}}{\theta_{y}} =$
A) 1
B) 2
C) 4
D) 16
Explanation
(d) $\tau_{x} = \ \frac{\pi\eta r^{4}}{2l}\ \theta_{x}\ \ \ and\ \ \ \tau_{y} = \ \ \frac{\pi\eta(2r)^{4}}{2l}\theta_{y}$
Since, $\tau_{x} = \ \ \tau_{y},$
$\therefore\ \ \theta_{x} = 16\theta_{y}\ \ \ \ or\ \ \frac{\theta_{x}}{\theta_{y}} = 16$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.