Enable contrast version

Tutor profile: Darshak M.

Inactive
Darshak M.
Graduate from Indian Institute of Technology, Kharagpur
Tutor Satisfaction Guarantee

Questions

Subject: Mechanical Engineering

TutorMe
Question:

Stress must increase with an increase in strain. But that's not always the case. In materials like steel, the stress decreases after the upper yield point. Why does steel have an upper as well as a lower yield point?

Inactive
Darshak M.
Answer:

Materials such as steel are added with impurities like carbon to alter their properties. Dislocations exist in all of the materials but impurities block the movement of these dislocations. For unlocking the dislocations higher stress is required resulting in the upper yield point. But once the dislocations start unlocking it is a rapid process decreasing further stress resulting in the lower yield point.

Subject: Calculus

TutorMe
Question:

Find the value of the integral, $$ \int_0^5 \int_0^5 \lfloor x+y \rfloor\mathrm{d}x\mathrm{d}y $$ where $$ \lfloor.\rfloor $$ indicates floor function.

Inactive
Darshak M.
Answer:

I = $$ \int_0^5 \int_0^5 \lfloor x+y \rfloor\mathrm{d}x\mathrm{d}y $$ Using the laws of integration, I = $$ \int_0^5 \int_0^5 \lfloor 5-x+5-y \rfloor\mathrm{d}x\mathrm{d}y $$ = $$ \int_0^5 \int_0^5 \lfloor 10-x-y \rfloor\mathrm{d}x\mathrm{d}y $$ Adding these equations, 2I = $$ \int_0^5 \int_0^5 \lfloor x+y \rfloor\mathrm{d}x\mathrm{d}y $$ + $$ \int_0^5 \int_0^5 \lfloor 10-x-y \rfloor\mathrm{d}x\mathrm{d}y $$ 2I = $$ \int_0^5 \int_0^5 (\lfloor x+y \rfloor+\lfloor 10-x-y \rfloor)\mathrm{d}x\mathrm{d}y $$ if x+y in non integer, $$ (\lfloor x+y \rfloor+\lfloor 10-x-y \rfloor) $$ = 9 When x+y is negative the area under the curve at those points is quite negligible. So final integral becomes 2I = $$ \int_0^5 \int_0^5 9\mathrm{d}x\mathrm{d}y $$ = 225 I = 225/2

Subject: Physics

TutorMe
Question:

You are walking peacefully in the street enjoying the cold, chilly weather. For some reason, you look above your head and see a bunch of mosquitoes hovering over your head. You try to run away from them but adamant as they are, mosquitoes catch you up. What do you think is the reason for the hovering of mosquitoes over the head?

Inactive
Darshak M.
Answer:

Biology: Mosquitoes are cold-blooded animals. So they need an external medium to regulate their temperature for better development. Mosquitoes' body includes heat sensors around its mouth to detect the warmth of the body. But why hover over the head? Physics: Due to the temperature difference between the human body and atmosphere, heat transfer takes place. The density gradient is induced in the fluid(in this case air) due to temperature gradient resulting in a buoyant force. This is called Free/Natural convection mode of heat transfer. The human head acts as a spherical body. The boundary layer due to free convection starts to develop from the bottom increasing the thickness along the circumference to the top resulting in plume formation. This plume attracts the mosquitoes.

Contact tutor

Send a message explaining your
needs and Darshak will reply soon.
Contact Darshak

Request lesson

Ready now? Request a lesson.
Start Lesson

FAQs

What is a lesson?
A lesson is virtual lesson space on our platform where you and a tutor can communicate. You'll have the option to communicate using video/audio as well as text chat. You can also upload documents, edit papers in real time and use our cutting-edge virtual whiteboard.
How do I begin a lesson?
If the tutor is currently online, you can click the "Start Lesson" button above. If they are offline, you can always send them a message to schedule a lesson.
Who are TutorMe tutors?
Many of our tutors are current college students or recent graduates of top-tier universities like MIT, Harvard and USC. TutorMe has thousands of top-quality tutors available to work with you.
BEST IN CLASS SINCE 2015
TutorMe homepage
Made in California by Zovio
© 2020 TutorMe, LLC
High Contrast Mode
On
Off