Math Chapter Wise

EnglishUPPSC GDC 2021

Q41.The relativistic form of Newton's second law of motion is

A2 2 2 mc dv F c v dt = − B2 2 m c v dv F c dt − = C2 2 mc dv F dt c v = − D() 2 2 2 m c v dv F c dt − =

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q42.If ABCD is a rectangle and AB=2a, AD=2b, then the inclination of AB of one of the principal axes at A is-

A–1 2 2 1 2ab tan 2 a – b B–1 2 2 1 3ab tan 2 2(a – b) C–1 2 2 1 ab tan 2 2(a – b) DNone of the above

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EnglishUP Higher Asst. Prof. 2021

Q43.Turbulence problem particularly depend on the term of the Navier Stokes equations which is the

Arate of change term Bconvection term Csource term Ddiffusion term

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EnglishUP Higher Asst. Prof. 2021

Q44.The Lagrangian for a charged particle in a electromagnetic field is -

AL = T – qφ + q(ν.A) BL = T + qφ + q(ν.A) CL = T – qφ – q(ν.A) DL = T + qφ – q(ν.A)

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EnglishUP Higher Asst. Prof. 2021

Q45.The constraints on bead on a uniformly rotating wire in a force free space is

ARheonomous BScleronomous CNo Constraints DNone of these

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EnglishUP Higher Asst. Prof. 2021

Q46.A surface that is every where tangent to both flow velocity and vorticity is called

Aa steady tube Ban angular tube Ca vortex tube DNone of these

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EnglishUPPSC GDC 2021

Q47.Given K.E. = T = i 2 1 mr 2 and P.E. = V= i 2 2 1 r 1+ 2 c, then Hamiltonian H =?

AT + V BT + V 2 2r c + i CT + V 2 2r – rc i DT + V 2 2r rc + i

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q48.The Lagrange's equation of motion of simple pendulum is-

A2 d g sin 0 dt θ + θ = l B2 d 2g sin 0 dt θ + θ = l C2 d g sin 0 dt θ + θ = 2l D2 d g sin 0 dt θ + θ = l

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q49.If A, B and C denote the moment of inertia about any three rectangular axes meeting at a given point, then which of the following is NOT correct?

AA+C>B BB+C>A CA+B+C=constant D(A+B+C) is equal to the moment of inertia about the given point.

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q50.If the Lagragian does not depend on the time explicitly, then-

AThe kinetic energy is constant BThe potential energy is constant CThe Hamiltonian is constant DThe Hamiltonian cannot be constant

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q51.For two systems to be equi-momental, the following conditions- I: They have same total mass II: They have same centroid III: They have same principal axes are-

Anecessary only Bsufficient only Cnecessary and sufficient Dneither necessary nor sufficient

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q52.For the Lagrangian i i 2 2 L = ax + by – cxy, the Hamilton H is-

A2 y x p cxy 2a 2y + + B2 y x p cxy 4a 4b + + C2 y x 2 2 p cxy 4a 4b + + D2 2 x y p p cxy 4ab +

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q53.The equation of momental ellipsoid at the centre of elliptic plate with mass 'M' and semi axes 'a' and 'b' is-

A() 2 2 2 2 2 2 b x y z (b a) constan t + + + = B() 2 2 2 2 2 2 a x y z (b a) constan t + + + = C2 2 2 2 2 2 2 a x b y z (b a) constan t + + + = D2 2 2 2 2 2 2 b x a y z (b a) constan t + + + =

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q54.A particle of mass 'm' is constrained to move in a vertical plane along a trajectory given by x=Acosθ, y=Asinθ, where 'A' is constant. The Lagrangian of the particle is-

A2 1 mA – mgAcos 2 θ i B2 1 mA mgAcos 2 θ + θ i C2 1 mA mgAsin 2 θ + θ i DNone of the above

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q55.The moment of inertia of an elliptic plate 2 2 x y + a b =1 about an axis through its centre and perpenducular to it is given by (M is the mass of the body)-

A2 2 M(a b) + B() 2 2 M a b 2 + C() 2 2 M a b 3 + D() 2 2 M a b 4 +

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q56.If the time of a complete oscillation of compound pendulum is 2 k 2π gh then the length of simple equivalent pendulum is-

A2 k g B2 k h C2 k gh Dk/h

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q57.A straight uniform rod of length 'a' can turn freely about its one end O, hangs from O vertically. The least angular velocity with which it must begin to move, so that it may perform complete revolution in a vertical plane is-

A6g/a B5g/a C7g/a DNone of the above

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q58.The number of degree of freedom of rigid body moving freely in space is-

A2 B3 C4 D6

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EnglishUPPSC Polytechnic Lecturer 2021 (I)

Q59.Moment of inertia of a uniform rod of length '2a' and mass 'm' about a line perpendicular to rod through the centre of mass is-

A2 1 ma 2 B2 1 ma 3 C2 1 ma 4 DNone of these

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EnglishUPPSC Polytechnic Lecturer 2021(II)

Q60.If 'H' is the Hamiltonian and 'f' is any function depending on position, momenta and time, if [H, f] is the Poisson Bracket, then -

Adf f [H,f ] dt t ∂ = + ∂ Bdf f [H,f ] dt t ∂ = − ∂ Cdf f [H,f ] dt t ∂ = − + ∂ DNone of these

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