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  4. The torque required to produce a unit twist in a rod of length l and radius r is (1) directly proportional to r2 (2) directly proportional to r4 (3) inversely proportional to r2 (4) inversely proportional to l

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Q. 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 $l$

BHUBHU 2009

Solution:

$\tau=\frac{\pi \eta r^{4}}{2 l} , \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.