CLEAR
Toprankers-Info

+91 7676564400

Mobile App

Get it on Google Play
Discussions
Select Date
Tags:

Articles

Discussions
Submit Discussion
ANIL KUMAR DESAI

· started a discussion

· 1 Months ago

wrong question (Question: 331512.0 )

it will be maximum not minimum

Question:

Minimum shear strain in orthogonal turning with a cutting tool of zero rake angle is

Options:
A)

0.0

B)

0.5

C)

1.0

D)

2.0

  

Solution:

Ans: (d)

 

Knowledge Expert

· commented

· 1 Months ago

Dear Student
∝ = 0°

Shear strain s=cotϕ+tan(ϕ−α)s=cotϕ+tan(ϕ−α)

⇒s=cotϕ+tanϕ⇒s=cotϕ+tanϕ

for minimum value, dsdϕ=0dsdϕ=0

⇒−cosec2ϕ+sec2ϕ=0⇒−1sin2ϕ+1cos2ϕ=0⇒cos2ϕ−sin2ϕ=0⇒cos2ϕ=0⇒ϕ=π4⇒−cosec2ϕ+sec2ϕ=0⇒−1sin2ϕ+1cos2ϕ=0⇒cos2ϕ−sin2ϕ=0⇒cos2ϕ=0⇒ϕ=π4

again d2sdϕ2=−2cosecϕ×(−cosecϕ.cotϕ)+2secϕ×(secϕ.tanϕ)d2sdϕ2=−2cosecϕ×(−cosecϕ.cotϕ)+2sec⁡ϕ×(sec⁡ϕ.tan⁡ϕ)

at =π4,d2sdϕ2=2cosec2(π4)cot(π4)+2 sec2π4tanπ4=π4,d2sdϕ2=2cosec2(π4)cot⁡(π4)+2 sec2π4tan⁡π4

= 2 × 2 × 1 + 2 × 2 × 1 = 8 > 0

So, minimum value at ϕ=π4ϕ=π4

then S(min)=cotπ4+tanπ4=1+1=2
Thanks and Regards
Team TopRankers
-logo
We at aim to provide most comprehensive content & test for practice which is carefully divided into various chapters and topics to help you focus on your weak areas.Our Practice mock test gives you unmatched analytics to help you realize your strong areas,time management and improvement areas.Our Short & Crisp notes on each topic will help you to quickly revise the topic along with the tips & tricks of the exams.
More About
-Info
-Info

Mobile App

Get it on Google Play
About Us Campus Ambassador Careers Contact Us Refund Policy

All Rights Reserved Top Rankers

User Policy
Disclaimer
Terms & Conditions