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Q2.
J =3mv/2
frictional impulse= μJ = 3μmv/2
therefore velocity is v/2(given in perpendicular direction) and μ3v/2 in tangential direction.
Torque due to frictional impulse = μJR = 3μmvR/2
3μmvR/2=2/5mR2(ω+ω0).. say final ω is in direction opposite to initial..
ω=(15μv/4R)-ω0... in opposite sense as initial ω...
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33
Abhishek Priyam
·2009-02-01 21:35:13
Q.4)
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N=(mg+F)
μN=ma...... a=αR
μ(mg+F)=mαR ...(i)
(F-μN)R=mR2/2α
(F-μmg-μF)=m/2(αR).... (ii)
From (i) and (ii)
(F-μmg-μF)=(μmg+μF)/2
F=(3μmg)/(2-3μ)....
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hmmm.... amazingly whats special about μ=2/3.... [12]
33
Abhishek Priyam
·2009-02-01 21:36:48
I think rest u should solve.. :P
143) mu=1/2. n friction=4.48N ????????????
and acceleration of M = 7X1.12/5 ????????????????
106Ans given for 43 are 3.75m/s2, 12N and ang accn of cylinder = 30rad/s2 (clockwise)
1hey guyzzz the answer for Q.2 is 1/2 am i rite???????!!!!!!!!!!!
106
Asish Mahapatra
·2009-02-02 07:47:24
@Abhisek: For Q1. why is dτ=M μ g 2πx2dx
Î R2
33
Abhishek Priyam
·2009-02-02 09:13:46
(m/Ï€iR2)2Ï€xdx is mass of ring...
and μdmgx = torque... (x is distance of that ring.)
106
Asish Mahapatra
·2009-02-01 07:42:17
in terms of w (initial) and v
33
Abhishek Priyam
·2009-02-04 21:21:48
Q43.
Draw FBD and i think it should be easy..
106
Asish Mahapatra
·2009-02-04 21:25:26
please solve it. i am not able to properly write the torque eqn.
33
Abhishek Priyam
·2009-02-04 21:27:59
Q.52..
part a) is hint for part b)
Notice that no force acts on rod in horizontal direction (as surface is smooth..)so acom in horizontal direction is 0. initially vcom =0 in horizontal direction so it(COM) will fall in straight line...
for part b)
ωlcosθ = vcom
2
mgl/2-mgl/2(sinθ)=1/2mvcom2+(1/2)(ml2/12)ω2
solve it to get the answer..
33
Abhishek Priyam
·2009-02-04 21:29:57
hmm... post whatever u have done in that.. it would be more beneficial...
33
Abhishek Priyam
·2009-02-04 21:37:40
For Q. 52 if its not clear..
see: http://targetiit.com/iit_jee_forum/posts/fjee_aits_rotation_2052.html
1
skygirl
·2009-02-05 20:10:08
areyyyyyyyyyy!!! mereko yeh q.1 ka case abhi samajh me aya ...!!
lol!
i have been thnking from day1 ki the disc is vertical ...
figure hi nahi chamka ...
aaj chamka!
[3] [3]
and abhiisekh, u drew it in such a way as if it is vertical...
and i had bn thinking from that day... yeh kaisa question hai! vertically ghoomra aur friction flat portion pe act karra!
hey gv fig along wid questions re!
1http://www.goiit.com/upload/2009/2/2/05bc183d08fe220370c490fde69d3e22_70619.png
33
Abhishek Priyam
·2009-02-01 04:54:15
man koi itna question ek topic ka kaise bana sakta hai... all same ones.. i solved only first one .. :P
106
Asish Mahapatra
·2009-02-01 04:28:02
Q3. A perfectly rough inelastic sphere of radius a is rolling with velocity v on a horizontal plane when it meets a fixed obstacle of height h. Show that if a√70gh/(7a-5h)<v<7a√(a-h)g/(7a-5h) then the sphere will overcome the obstacle.
106
Asish Mahapatra
·2009-02-01 04:38:59
A uniform solid cylinder of mass m rests on two horizontal planks. A thread is wound on the cylinder. The hanging end of the thread is pulled vertically down with a constant force F. Find the maximum magnitude of the force F which still does not bring about any sliding of the cylinder, if the coefficient of friction between the cylinder and the planks is equal to k.
106
Asish Mahapatra
·2009-02-01 04:48:43
sky all ur answers are wrong :(
106
Asish Mahapatra
·2009-02-01 04:53:26
yup abhisek. cud u show working
106
Asish Mahapatra
·2009-02-01 04:23:56
Q2. A rotating ball hits a rough horizontal plane with a vertical velocity v and angular velocity ω. Given that the coefficient of friction is μ and the vertical velocity of the ball after the collision is v/2, find the angular velocity after collision.
106
Asish Mahapatra
·2009-02-01 04:55:12
A disc rolls upon a straight line on a horizontal table, the flat surface of the disc being in contact with the table. If be the velocity of the center of the disc at , find the time after which the disc comes to rest. Given the coefficient of friction between the disc and the table is:
