Mechanics - mechanics.. again

1

hacker ·2010-02-03 23:40:06

@asish

can u tell me what is wrong with answer i gAVE FOR Q.1?????

WAT IS ANSWER GIVEN??????

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23

qwerty ·2010-02-06 21:00:16

only 1 ans is correct , rest 2 not matching [2]

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49

Subhomoy Bakshi ·2010-02-04 04:42:40

arre that wat i wanted to say

there is no need 4 manipulations..

work done=-(potential energy stored)

[1][1][1]

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106

Asish Mahapatra ·2010-02-04 03:21:08

yeah even i was getting that for Q1. But the answer is given as -0.5kx² [11]

@jamesbond: hmm now dat u mention it .. i think the vector will change if u change the reference frame [12]

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106

Asish Mahapatra ·2010-02-04 03:12:06

the answer given is x=2 [2]

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23

qwerty ·2010-02-04 01:28:56

thus from 1 and 2 ,

b = 0

thus tan \theta _{o} = 0

thus x/3 = 0

thus x = 0

wats d ans ?

PS: (1)\theta _{o} = \theta'

(2) in second case since frame of man = frame of grnd , v_r/g = v_r/m in d third case

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1

Arka Halder ·2010-02-04 00:27:47

oh yeah.small mistake.
it will be
Xcom=(V₁x₁-V₂x₂)/V₁-V₂
where V₁=vol of initial sphere
x₁=abssica of com of initial sphere
V_₂=vol of cut out sphere
x₂ =abssica of com of cut out sphere
Xcom=(-R⁴/16)/7R³/8
=-R/14

So coordinates of com=(-R/14,0,0) ans has to be this one!

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1

hacker ·2010-02-04 00:21:16

@asish

answer updated in #4

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23

qwerty ·2010-02-04 00:11:21

arka , it is a sphere here, not a disc !!

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1

Arka Halder ·2010-02-04 00:09:14

ans 2 has to be (-R/6,0,0).had done it lot earlier,still remember the ans.

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23

qwerty ·2010-02-03 23:59:22

i havent used it here ,

btw can u post ur method

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1

hacker ·2010-02-03 23:57:54

displaced through x means displaced through x wat's the problem qwerty?????

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1

hacker ·2010-02-03 23:49:24

@QWERTY

BE ASSURED BEGINNING ITSLEF IS WRONG [1]
COZ I DON'T THINK anything is said in question about [3][3]final velocity as being zero[3][3].............lolz

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23

qwerty ·2010-02-03 23:47:23

W_{spring}= \frac{k}{2}[(L+x-h)^{2}-(L-h)^{2}]

W_{spring}= \frac{k}{2}[(\frac{Mg+F}{k})^{2}-(\frac{Mg}{k})^{2}]

W_{spring}= \frac{k}{2}[\frac{2Mg+F)(F)}{k^{2}}]

W_{spring}=\frac{(2Mg+F)(F)}{2k}

W_{spring}=\frac{MgF}{k}+\frac{F^{2}}{2k}

W_{spring}=Mgx+\frac{1}{2}kx^{2},\;\; i.e\;\; put\;\; F =kx

since F= kx from 1 and 2

PS: ANS IS NEGATIVE OF WAT I HAV GIVEN , FOGOT THE MINUS SIGN IN LATEX

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1

hacker ·2010-02-03 23:43:57

@ASISH,SUBHOMOY,ANIRUDH,ETC..........[WHO FAVOUR B,D FOR Q.4]

ASISH U SAID CLEARLY D IS TRUE[3]
AND I SAY ONLY B IS TRUE

OK AN EXTENSION TO THE QUESTION NO. 4
TRY TO FIND ANY EXMPLE TO SAY THAT OPTION D IS NOT ALWAYS CORRECT...

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39

Dr.House ·2010-02-03 06:46:33

1) f+mg=kx

=(f+mg)/k

this gives us expansion.. now u can find the work done

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1

hacker ·2010-02-03 23:39:14

@asish

y question 3 is unsolved????????? i gave answer as 0[zero][shunya]///////isn't it right??????????

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23

qwerty ·2010-02-03 22:43:37

let mass of sphere = M

mass of smaller sphere = M_a = \frac{(R/2)^{3}}{R^{3}}M= \frac{M}{8}

assume the centre of larger sphere to be (0,0,0)

obviously y and z coordinates of COM arent changing

M_{a}x_{a}+M_{b}x_{b} = M x_{cm}

where M_a =mass of smaller sphere

M_b= mass of remaining sphere

x_a = psoition vector of COM of smaller sphere

x_b = position vector of COM of remaining part

x_cm = radius vector of centre of larger sphere = 0

hence

M_{a}x_{a}= - M_{b}x_{b}

x_{b}= -\frac{M_{a}x_{a} }{M_{b} }

x_{b}= -(\frac{\frac{M}{8}x_{a} }{M-\frac{M}{8} })

clearly x_a = R/2

x_{b}= -(\frac{\frac{MR}{8\times 2} }{\frac{7M}{8}} )

\Rightarrow x_{b}= -\frac{R}{14}

hence COM of remaining part is (\frac{-R}{14},0,0)

oh ok , COM of larger sphere is already given to be [0,0,0], dint notice dat

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1

pranav ·2010-02-03 21:46:03

in the second one u have to use...

A_CM = ( A₁R₁ - A₂R₂)/(A₁-A₂)

WHere R1 IS com of bigger sphere and R2 is COM For secind sphere and as it is sphere so u can prob . use volume.

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106

Asish Mahapatra ·2010-02-03 20:07:43

@subhomoy: explain Q4 .. C (BD are obviously true)

@jamesbond : explain Q2... (ur answer's correct)

Q1. no one is correct according to the options given

q3. unsolved

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1

lalit ·2010-02-03 19:30:01

Ans4-b,d

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49

Subhomoy Bakshi ·2010-02-03 10:42:53

4) b,c,d...[7][7][7]

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49

Subhomoy Bakshi ·2010-02-03 10:40:26

yeah forgot to mention, in the above problem y=0 due to symmetry...or we can also use the equation...

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49

Subhomoy Bakshi ·2010-02-03 10:39:33

2) 3M.(x)+M.(^R/₂)=(4M).(0)
=>x=--^R/₆

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1

hacker ·2010-02-03 08:43:15

sorry for the above nonsense i know i m wrong in all above questions ..........plz can u guys suggest me a workout plan for remaining days left for jee i mean what should i do in next few days tyo make optimum use of remaining time and atleast get the last rank in jee.................i know i m tooooooo late and i don't desrve to get into iit but plz suggest something to this fool ...................i wanna try my luck!!!!!!plz help!!!!!!