|

Mechanics

New kid on the Block

 Joined: 16 Aug 2011 Post: 1
16 Aug 2011 20:33:58 IST
0 People liked this
2
897
Newton's Laws of Motion
Engineering Entrance , Medical Entrance , NEET , JEE Main , AIIMS , JEE Main & Advanced , Physics , Mechanics , Kinematics , NewtonsLawsCirMotion , Work Power EnergyÂ collisions , Rotation , Gravitation , Simple Harmonic Motion , Fluid Mechanics , Materials Wave Sound , Super Position , units dimensions , com momentum , shm , wave sound

An insect is crawling up a hemispherical bowl of radius R. If the coefficient of friction is 1/3, then upto what height will it be able to crawl? (a)R/5 (b)R/10 (c)R/20 (d)R/30

Blazing goIITian

Joined: 27 Dec 2010
Posts: 1508
26 Aug 2011 11:07:37 IST
0 people liked this

let the insect crawl upto a height h.

also let the point on the surface of the hemishphere at the height h be P.

the center of circular upper portion be O and the point directly below it on the hemisphere be S.

then, there must be a point N on OS such that NS = h. such that ON = (r-h).

also a triangle is formed by O , N and P such that OP = r. let the vertical angle be x in this rigth angled triangle. that is angle PON is x. and ONP = 90 degrees.

also since the insect at the heighest point will be in equilibrium so, there Wsinx = k(Wcosx) where x is the coefficient of friction or 1/3.

so, on solving we get, tanx = k = 1/3

but tanx = (PN)/(ON)

but, if ON = r-h and PN = sqrt[r2 - (r-h)2]

on putting the values and solving we get,

9[r2-(r-h)2] = (r-h)2

or, 3r = sqrt[10](r-h)

or, (sqrt10r - 3r)/sqrt[10] = h

so, h = 0.05r

Forum Expert
Joined: 19 Feb 2009
Posts: 1958
26 Aug 2011 18:37:00 IST
0 people liked this

A good Solution !

 Some HTML allowed. Keep your comments above the belt or risk having them deleted. Signup for a avatar to have your pictures show up by your comment If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team

For Quick Info

Name

Mobile

E-mail

City

Class

Vertical Limit

Top Contributors
All Time This Month Last Week
1. Bipin Dubey
 Altitude - 16545 m Post - 7958
2. Himanshu
 Altitude - 10925 m Post - 3836
3. Hari Shankar
 Altitude - 10085 m Post - 2217
4. edison
 Altitude - 10825 m Post - 7804
5. Sagar Saxena
 Altitude - 8635 m Post - 8064
 Altitude - 6330 m Post - 1958

Physics

Topics

Mathematics

Chemistry

Biology

Institutes

Parents Corner

Board

Fun Zone