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[k.Mksa d rFkk [k esa foHkkftr gSA izR;sd [k.M esa fn, x, foLr`r funsZ'kksa ds vuqlkj gh iz'uksa dks gy dhft,A

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mt-09 mechanics

;kaf=kdh

Bachelor of Science (BA/BSC-12/16) Third Year, Examination-2020

Time Allowed : 2 Hours Maximum Marks : 40 note: This paper is of Forty (40) marks divided

into Two (02) sections A and B. Attempt the question contained in these sections according to the detailed instructions given therein.

uksV% ;g iz'u i=k pkyhl

(40)

vadksa dk gSA tks nks

(02)

[k.Mksa d rFkk [k esa foHkkftr gSA izR;sd [k.M esa fn, x, foLr`r funsZ'kksa ds vuqlkj gh iz'uksa dks gy dhft,A

section-a/

[k.M&^d*

(Long Answer Type Questions/

nh?kZ mÙkjh; iz'u)

Note: Section-'A' contains Five (05) long answer type questions of Ten (10) marks each. Learners are required to answer any two (02) questions

only. (2×10=20)

(2)

uksV% [k.M&^d* esa ik¡p (05) nh?kZ mÙkjh; iz'u fn, x, gSa] izR;sd iz'u ds fy, nl (10) vad fu/kZfjr gSaA f'k{kkfFkZ;ksa dks buesa ls dsoy nks (02) iz'uksa ds mÙkj nsus gSaA

1. Find Moment of inertia of a solid sphere about its diameter.

,d Bksl xksys dk mlds O;kl ds lkis{k tM+Ro vk?kw.kZ Kkr dhft,A

2. Find differential equation F h dp23

=p dr for central orbit in pedal form.

ladsUnz d{kk dk ifnd :i esa

F=h dpp dr23

vodyu lehsdj.k izkIr dhft,A

3. Four equal heavy uniform rods are freely joined so as to form a rhombus which is freely suspended by one angular point and the middle points of the two upper rods are connected by a light rod so that the rhombus cannot collapse. Prove that the tension in this light rod is uw tan α, where w is the weight of each rod and is the angle of the rhombus

(3)

pkj leku Hkkj le NM+ksa dks eqDr :i ls tksM+dj ,d leprqHkqZt cuk;k x;k gS tks ,d dksus ls LorU=k :i ls yVdk gSA Åijh NM+ksa ds eè; fcUnqvksa dks ,d gYdh NM+ ls tksM+k x;k gS rkfd leprqHkZqt cuk jgsA fl¼ dhft, fd gYdh NM+ esa ruko

uw tan α

gksxk] tgk¡

w

izR;sd NM+ dk Hkkj gS rFkk

fuyEcu fcUnq ij dks.k gSA

4. Obtain the equation of a uniform common catenary in the form S = C s c Sin hx

= c, where symbols have their usual meanings.

,d lkekU; loZ=kle jTtq oØ ds fy, lehdj.k

S = C s c Sin hx

= c

dks fudkfy,] tgk¡ izrhdksa ds ;Fkkor vFkZ gSaA

5. Discuss Motion of a particle on the inside of a smooth vertical circle.

,d fpdus ÅèokZ/j o`r ds vUr% ry ij d.k dh xfr

dk mYys[k dhft,A

(4)

section-B/

[k.M&[k

(Short answer type questions/

y?kq mÙkjh; iz'u)

Note: Section-B Contains Eight (08) short answer type questions of Five (05) marks each. Learners are required to answer any four (04) questions

only. (4×5=20)

uksV% [k.M&^[k* esa vkB (08) y?kq mÙkjh; iz'u fn, x, gSa] izR;sd iz'u ds fy, ik¡p (05) vad fu/kZfjr gSaA f'k{kkfFkZ;ksa dks buesa ls dsoy pkj (04) iz'uksa ds mÙkj nsus gSaA

1. If two forces P and Q acts at a point and α is included angle then resultant R is given by R2 = P2 + Q2 + 2PQG α and angle θ which resultant make with P can be given by

tan θ= Q sinP QG+Q cos αα α

(5)

;fn ,d fcUnq ij yxs nks cyksa

P

o

Q

ds eè; dks.k

α

gks rFkk budk ifjek.kh

R

rc

R2 = P2 + Q2 + 2PQG α

rFkk ifj.kkeh o

P

ds eè; dks.k

θ

fuEu izdkj gksxk

tan θ= Q sinP QG+ αα

2. Discuss forces which can be omitted while forming equation of Virtual wak.

mu cyksa dk mYys[k djsa tks cy dfYir dk;Z ds lehdj.k fuekZ.k djrs le; NksMs+ tk ldrs gSaA

3. If radial and transverse velocity of a particle is

2 2

r and Q

λ µµθ2 then prove that equation of the path of the particle is 2 C

2r λ = µ +

θ .

fdlh d.k ds vjh; rFkk vuqizLFk osx Øe'k%

2 2

r and Q

λ

rFkk

µµθ2

gSA fl¼ dhft, fd d.k ds iFk dk lehdj.k

λθ = 2rµ2 + C

gksxkA

4. Discuss Kepler's law.

dsIyj ds fu;eksa dks crykb,A

Q cos α

(6)

5. For central orbit show that

2

2 h u2 2 du

ϑ = +dq

ladsUnz d{kk ds fy, fl¼ dhft, %

2

2 h u2 2 du

ϑ = +dq

6. For Common catenary show that : (T y)α

,d le:i dSVujh ds fy, fl¼ dhft, %

(T y)α

7. Find the Cartesian Equation of Catenary.

jTtq oØ dk dkrhZ; lehdj.k Kkr dhft,A

8. Write necessary and Sufficient Conditions of equilibrium of a particle under the action of a system of forces.

,d d.k ij fudk; cyksa ds fy, larqyu dh fLFkfr ds fy, i;kZIr o vko';d 'krks± dks fyf[k,A

*******

θ

θ

References

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