If ρ is the density of the material of a uniform rod and σ is the breaking stress, and the length of the rod is, such that the rod is just about to break due to its own weight when suspended vertically from a fixed support, then:

Book Online Demo

Check Your IQ

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

If $ρ$ is the density of the material of a uniform rod and $σ$ is the breaking stress, and the length of the rod is, such that the rod is just about to break due to its own weight when suspended vertically from a fixed support, then:

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

Stress at all horizontal sections of the rod is same

The rod is about to break from its mid point

Length of the rod is $\frac{σ}{ρ g}$

Stress at a cross section perpendicular to the rod, at one fourth the length of the rod above its lowest point is $\frac{σ}{4}$

answer is A, B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

The stress is max at the uppermost point and is equal to the weight of the rod divided by the area. At the highest point stress = breaking stress = $σ$ = weight of rod/area of cross section of the rod $= \frac{A L ρ g}{A} = L ρ g$ .
$∴ L = \frac{σ}{ρ g}$ .
The stress decreases linearly to zero at the lowest end.