Question

The torque required to produce a unit twist in a rod of length $l$ and radius $r$ is
(1) directly proportional to $r^2$
(2) directly proportional to $r^4$
(3) inversely proportional to $r^2$
(4) inversely proportional to $l$

• A. 1, 2 and 3 are correct
• B. 1 and 2 are correct
• C. 2 and 4 are correct
• D. 1 and 3 are correct

Answer 1

Answer: (C)

$\tau =\frac{\pi \eta r^4}{2l},\tau \propto r^4\text{ and }\tau \propto (1/l)$
where $\eta =$ modulus of rigidity
$r=$ radius of rod
$l=$ length of rod
Other, central maximum thus shifts vertically downward and so, do the other fringes.