Classical Mechanics MCQ PDF

lOMoARcPSD|48187727 Classical Mechanics MCQ Number theory (University of Education) Scan to open on Studocu Studocu is not sponsored or endorsed by any college or university Downloaded by RASAL SANSKRUTI ([email protected])  lOMoARcPSD|4818...

lOMoARcPSD|48187727 Classical Mechanics MCQ Number theory (University of Education) Scan to open on Studocu Studocu is not sponsored or endorsed by any college or university Downloaded by RASAL SANSKRUTI ([email protected])  lOMoARcPSD|48187727 CLASSICAL MECHANICS MCQS BS Mathematics Semester 6 Dr. Raza Ahmad Downloaded by RASAL SANSKRUTI ([email protected])  lOMoARcPSD|48187727 Multiple Choice Questions Classical Mechanics BS Mathematics(2017-2021) Lecture 1 1. Classical mechanics describes the motion of _______. (a)Microscopic object (b)Macroscopic object (c)None of the above (d)Both a and b 2. Abstract methods were developed leading to the reformulations of classical mechanics. (a)Lagrangian Mechanics (b)Hamiltonian Mechanics (c)Quantum Mechanics (d)Both a and b 3. The quantitative measure of inertia of a body is called ______. (a)Weight (b)Mass (c)Gravity force (d)None of these 4. The branch of physics which describes the conditions of rest or motion of material bodies around us under action of force is _______. (a)Mechanics (b)Mechatronics (c)Quantum field (d)None of these 5. The mass that determines the acceleration of a body under the action of a given force is called __. (a)First mass (b)Inertial mass (c)Reference mass (d)None of these 6. A particle is an object which has ______. (a)Mass (b)Size (c)Both a and b (d)None of these 7. Newton’s 1st law of motion is applicable for ______. (a)Free particles (b)Moving particles (c)Rest particles (d)None of these 8. Identify the correct number of types of reference frames. (a)3 (b)4 (c)5 (d)None of these 9. In curved space-time interval, all frames are _____. (a)Inertial (b)Non-inertial (c)Both a and b (d)None of these 10. Acceleration of an object depends on its ______. (a)Mass (b)Net force 1|P ag e Downloaded by RASAL SANSKRUTI ([email protected])  lOMoARcPSD|48187727 Multiple Choice Questions Classical Mechanics BS Mathematics(2017-2021) (c)Volume (d)None of these 11. Ratio of masses of two objects is equal to the negativity of _______. (a)Positive ratio of accelerations (b)Inverse ratio of accelerations (c)None of these (d)Both a and b 12. Linear momentum is conserved if ______ acting on a body is zero. (a)Net internal force (b)Internal force (c)Net external force (d)External force 13. Angular momentum is conserved if net torque acting on a body is _____. (a)Maximum (b)Zero (c)Uniform (d)None of these 14. Work energy principle can be written as ______. (a)Wab=∆T (b)Wa=T (c)Wab=T (d)Wt=∆T 15. The law of conservation of total energy states that (a)Ta + Va = Tb + Vb (b)Ta + Vb = Ta + Vb (c)Ta + Vb= Tb + Va (d)None of these Lecture 2 1. The conditions which restrict the motion of the system are called _____. (a)Constraints (b)Degree of freedom (c)Generalized coordinates (d)None 2. The number of independent ways in which a mechanical system can move without violating any constraint is called _____. (a)Constraint (b)Number of freedoms (c)Degrees of freedom (d)Generalized coordinates 3. A thing moving in space has ___ degrees of freedom. (a)1 (b)2 (c)3 (d)4 4. Work done by external force in N-particle system is known as ____. (a)Work (b)Total work (c)Virtual work (d)None of these 5. Total virtual work done on N-particle system is _____. 2|P ag e Downloaded by RASAL SANSKRUTI ([email protected])  lOMoARcPSD|48187727 Multiple Choice Questions Classical Mechanics BS Mathematics(2017-2021) (a)Zero (b)Maximum (c)Minimum (d)None 6. Virtual work is represented as ______. (a)δW = ∑Fei δri=0 (b)δW = ∑Few δri=0 (c)W = ∑FeI ri=0 (d)δW = ∑FeI δri 7. D ‘Alembert’s Principle can be written as (a)∑Ni=0 (Fl-pi). δri=0 (b)∑Ni=1 (Fl-pi). δri=0 (c)∑Ni=1 (Fl-p). δri=0 (d)∑Ni=1 (Fl-p). δr=0 8. In Lagrange’s Equation if there are N number of particles and so the generalized coordinated are (a)n=N-k (b)n=3N-k (c)n=3N (d)n=3n-k 9. In Lagrange’s Equation Virtual Displacement does not involve (a)Space (b)Time (c)N number of particles (d)None 10. Lagrangian function equation is known as 𝒅 𝝏𝑳 𝝏𝑳 𝑑 𝜕𝐿 𝜕𝐿 (a)𝒅𝒕 [ ]− = 𝟎 , 𝒋 = 𝟏, 𝟐, 𝟑 …. (b)𝑑𝑡 [ ]− , 𝑗 = 1,2,3 …. 𝝏𝒒𝒋 𝝏𝒒𝒋 𝜕𝑞𝑗 𝜕𝑞𝑗 𝑑 𝜕𝐿 𝑑 𝜕𝐿 𝜕𝐿 (c)𝑑𝑡 [ ] = 0 , 𝑗 = 1,2,3 …. (d)𝑑𝑡 [𝜕𝑞𝑗 ] − = 0, 𝜕𝑞𝑗 𝜕𝑞𝑗 11. Kinetic energy of a particle of mass m is a ___________ of the velocities (a)Quadratic function (b)Homogeneous quadratic function (c)Both a and b (d)None 12. The special case of kinetic energy of particle_______ does not appears in transformation equation (a)Space (b)Time (c)Both a and b (d)None 13. The special case of Euler’s Theorem is written as 𝝏𝒇 𝜕𝑓 (a)∑𝒌 𝐲𝐤 𝝏𝐲𝐤 = 𝒏𝒇 (b)∑𝑘 y 𝜕yk = 𝑛𝑓 𝜕𝑓 𝜕𝑓 (c)∑𝑘𝑖 yk 𝜕yk = 𝑛𝑓𝑖 (d)∑𝑘 yk = 𝑛𝑓𝑖 𝜕yk 14. The momentum of the moving particle in the x-axis is (a)P=1/2 mx (b)P= mx’ (c)P=mx (d)None 3|P ag e Downloaded by RASAL SANSKRUTI ([email protected])  lOMoARcPSD|48187727 Multiple Choice Questions Classical Mechanics BS Mathematics(2017-2021) 15. The generalized momentum PI need not always______ of linear momentum. (a)Speed (b)Velocity (c)Dimension (d)None Lecture 3 1. The Euler-Lagrange differential equation is written as 𝜕𝑓 𝑑 𝝏𝒇 𝒅 𝝏𝒇 (a)𝜕𝑦 − 𝑑𝑥 =0 (b)𝝏𝒚 − 𝒅𝒙 (𝝏𝒚) = 𝟎 𝜕𝑓 𝜕𝑓 𝑑 𝜕𝑓 (c)𝜕𝑦 − (𝜕𝑦 ) = 0 (d)𝑑𝑥 (𝜕𝑦 ) = 0 2. If the forces of the system are not conservative then the Lagrange’s equation will be 𝒅 𝝏𝑻 𝝏𝑻 𝑑 𝜕𝑇 𝜕𝑇 (a)𝒅𝒕 − 𝝏𝒒𝒊 = 𝑸𝒊 , 𝒊 = 𝟏, 𝟐, 𝟑 ….. (b)𝑑𝑡 − 𝜕𝑞𝑖 = 𝑄 , 𝑖 = 1,2,3 ….. 𝝏𝒒𝒊 𝜕𝑞𝑖 𝑑 𝜕𝑇 𝑑 𝜕𝑇 (c)𝑑𝑡 𝜕𝑞𝑖 = 𝑄𝑖 , 𝑖 = 1,2,3 ….. (d)𝑑𝑡 − 𝜕𝑞𝑖 = 𝑄𝑖 , 𝑖 = 1,2,3 ….. 3. The Lagrange’s equation for non-holonomic system is 𝑑 𝜕𝐿 𝜕𝐿 𝒅 𝝏𝑳 𝝏𝑳 (a) [ ]− = , 𝑗 = 1,2,3 …. 𝑛 (b) [ ]− = ∑𝒎 𝒊=𝟏 𝝀𝒊 𝒂𝒊𝒋 , 𝒋 = 𝟏, 𝟐, 𝟑 …. 𝒏 𝑑𝑡 𝜕𝑞𝑗 𝜕𝑞𝑗 𝒅𝒕 𝝏𝒒𝒋 𝝏𝒒𝒋 𝑑 𝜕𝐿 𝜕𝐿 𝑑 𝜕𝐿 𝜕𝐿 (c)𝑑𝑡 [𝜕𝑞 ] − 𝜕𝑞𝑗 = ∑𝑚 𝑖=0 𝜆𝑖 𝑎𝑖𝑗 , 𝑗 = 1,2,3 …. 𝑛 (d)𝑑𝑡 [𝜕𝑞 ] − 𝜕𝑞𝑗 = ∑𝑚 𝑖=1 𝜆𝑖 , 𝑗 = 1,2,3 …. 𝑛 𝑗 𝑗 4. In a plane, arc length of an element is (a)ds = (dx2 + dy2) (b)ds = (dx2 + dy2)1/2 (c)ds = (dx + dy)1/2 (d)ds = (dx + dy2)1/2 5. y=a x + b, b=constant is equation of (a)hyperbola (b)parabola (c)circle (d)straight line 6. T=__________ (a)1/2 m r θ (b)1/2 mr2.θ2 (c)1/2 mr2.θ (d)1/2 mr.θ2 7. V=________ (a)mg r cos θ (b)-mg cos θ (c)-mg r cos θ (d)–mr cos θ 8. The action integral must be a ________ value for actual path (a)Real (b)Stationary (c)Maximum (d)None 4|P ag e Downloaded by RASAL SANSKRUTI ([email protected])  lOMoARcPSD|48187727 Multiple Choice Questions Classical Mechanics BS Mathematics(2017-2021) 9. In configuration space by infinitesimal parameter path can be written as (a)qi(t, a)= qi(t, 0)+ah(t), i =1, 2, … (b)qi(t, a)= qi(t, 0)+ahi(t), i =1, 2, …, n (c)qi(t, a)= q(t, 0)+ahi(t), i =1, 2, …, n (d)qi(t, a)= qi(t, 0)+(t),i=1, 2, …, n 10. If y=y(x) then the equation becomes 𝑥 𝑑𝑦 𝒙 𝒅𝒚 (a)I=∫𝑥 2 𝑓(𝑦, 𝑥)𝑑𝑥 𝑦 = 𝑑𝑥 (b)I=∫𝒙 𝟐 𝒇(𝒚, 𝒚̇ , 𝒙)𝒅𝒙 𝒚̇ = 𝒅𝒙 1 𝟏 𝑥 𝑑𝑦 𝑥 (c)I=∫𝑥 2 𝑓 (𝑦̇ , 𝑥)𝑑𝑥 𝑦̇ = 𝑑𝑥 (d)I=∫𝑥 2 𝑓(𝑦, 𝑦̇ , 𝑥)𝑑𝑥 1 1 11. The length of any curve between points 1 and 2 is given by 2 𝑥 𝑑𝑦 2 𝑥 (a)𝐼 = ∫1 𝑑𝑠 = ∫𝑥 2 √1 + ( ) (b)𝐼 = ∫1 = ∫𝑥 2 √1 + (𝑑𝑦/𝑑𝑥)2 1 𝑑𝑥 1 2 𝑥 𝟐 𝒙 (c)𝐼 = ∫1 𝑑𝑠 = ∫𝑥 2 √(𝑑𝑦/𝑑𝑥)2 (d)𝑰 = ∫𝟏 𝒅𝒔 = ∫𝒙 𝟐 √𝟏 + (𝒅𝒚/𝒅𝒙)𝟐 1 𝟏 12. ℓ θ + g θ=_____ (a)0 (b)1 (c)2 (d)θ 13. The δ-variation considered refers to variation (a)Quantity (b)Time (c)Both a and b (d)None 14. 𝛿𝑞𝑖 = ________ (a)𝜂𝑖 𝛿𝛼 (b)𝜂𝑖 (t)𝛿 (c)𝜼𝒊 (t)𝜹𝜶 (d)(t)𝛿𝛼 15. 𝛿𝑞𝑖 (𝑡1 ) = 𝛿𝑞𝑖 (𝑡2 )= (a)0 (b)1 (c)𝛿 (d)None of these Lecture 4 Qno1: The simple mechanical system involving contriant is the atwoods mechine pully is assumed. a)Friction less b) mass less c)both a and b d) all of above Qno2: weight move vertically, we have only 5|P ag e Downloaded by RASAL SANSKRUTI ([email protected])  lOMoARcPSD|48187727 Multiple Choice Questions Classical Mechanics BS Mathematics(2017-2021) a)One degree of freedom b) two degree of freedom c three degree of freedom d) all of above Qno3: The length of the rope with which m2 is tied by a)1-q b) q1 c) m1 d) all of above Qno4: Two force are acting on each mass i.e weight acting a)Upward b) downward c) vertically d) all of above Qno5: The length of the rope with which m1 is tied by a)1-q b) q1 c) m1 d) all of above Qno6: Two forces are acting on each mass i.e. tension acting a)Upward b) downward c) vertically d) all of above Qno7: To determine the value of lagrangian L we assume a)Kinetic energy b) potential energy c)Both a and b d) all of above Qno8: The k.E of the system is a) T=1/2mivi^2 b) T=1/2mivi^2 6|P ag e Downloaded by RASAL SANSKRUTI ([email protected])  lOMoARcPSD|48187727 Multiple Choice Questions Classical Mechanics BS Mathematics(2017-2021) b) T=1/2m1v1^ +1/2m2v2^2 c) Both a and b d) d) T=1/2m2v2^2 -1/2m2v2^2 Qno9:Potential energy of the system is a)v=m1gh1 b) v=m1gh1 c) v=m1gh1 + v=m2gh2 d) both a and b Qno10:position of a point in cartesian coordinate [x,y,z] is given by a)Position of point= xi^ +yj^+zk^ b) Position of point= xi^ -yj^-zk^ C) r=sin(x) d) all of above Qno11: langrage’s equation of motion for a simple pendulum is ____. a) -(l)sin0=1 b) –(L/I)sin 0=o c) 0-(L/I)sin0 =o d) (L/I)sin =o Qno12: The K.E of ( simple pendulum ). a) T= ½ ml^20 b) b) T= ½ ml^2 0^2 c) c) T= ½ ml^2 d) d) all of above Qno13: potential energy of mass m is ( for simple. a)T=1/2ml^ T= ½ ml^2 b) T=1/2ml^0^2 c) T=1/2ml^2 d) none of these Qno14: In simple pendulum we take a horizontal plane passing through the a)Lowest point of mass b) Highest point of mass c) both a and b d)All of above Qno15: The equation of motion for spherical pendulum is. 7|P ag e Downloaded by RASAL SANSKRUTI ([email protected])  lOMoARcPSD|48187727 Multiple Choice Questions Classical Mechanics BS Mathematics(2017-2021) a) 0=-g/l (cos0 ) b) 0 =-g/l (sin0) c) 0=-g/l (cos 0) d) 0=g/l (cos) Lecture 5 Qno1: A force whose line of action always directed toward a fixed point is known as a) Central force motion b) Elliptical motion c) Both a and b d) None of these Qno2: In central force motion magnitude depends on. a)mass b)center c) origin d) all of above Qno3: examples of force motion are___. a)Gravitational force b)electrostatic force c) scattering of alpha b/w to charges d) all of above Qno4: The position vector of COM is a) R=r1-r2 b) R=m1r1+m2r2/m1+m2 c) Both a and b d) All of above Qno5: which one is the lagrangian equation of motion reduction one body problem. a)L=1/2ur^2 -(r) b) a)L=1/2ur^2 c) both a and b d) R=r1-r2 Qno6: In polar coordinate the lagrangian equation is. a) L= 1/2ur^2 b) b)L=1/2u(r^2+r^20^2) c) c) L=1/2u(r^2+r^2) 8|P ag e Downloaded by RASAL SANSKRUTI ([email protected])  lOMoARcPSD|48187727 Multiple Choice Questions Classical Mechanics BS Mathematics(2017-2021) d) d) all of above Qno7: If radical component if velocity and position vector are collinear then_____. a)|L|= ur^2(r0)= l b) ur^2(r0)= l c) L= 1/2ur^2 d) all of above Qno8: The area covered by a particle in a coordinate system is___. a)A=1/2r^20 b) A=1/2r^30 c) A=1/2r^30 d) all of above Qno9: How many way are used to find the motion of a particle in a central force field. a)Two b)Four c)Three Qno10: In energy method total energy of the system is___. a) E=1/2ur`^2 -L^/2ur^2 v(r) b) E=1/2ur`^2 c) Both a and b d) A=1/2r^30 Qno11: Which one is the differences equation of orbit ___. a) d^2(u)/d =u -1/L^2.f(1/u) b) d^2(u)/d =-u -1/L^2.f(1/u) c) d^2(u)/d =u1-1/L^2.f(1/u) d) d^2(u)/d =u3 -1/L^2.f(1/u) Qno12:In laws of equal areas the effective potential is equivalent to the effective ___. a)Force b)motion c) Both a and b d) all of above Qno13: Which are the ways to obtain the motion of a particle and a central force field. a) Energy method b) Lagrangian analysis c) Both a and b d) None of these 9|P ag e Downloaded by RASAL SANSKRUTI ([email protected])  lOMoARcPSD|48187727 Multiple Choice Questions Classical Mechanics BS Mathematics(2017-2021) Qno14:The reduce mass is defined as a) U=M1.M2/M1+M2 b) U=M1.M2/M1*M2 c) U=M1.M2/M1+M° d) None of these Qno15: In reduction to one body problem the kinetic energy of COM is defined on ___. a)1/2Mr`R^2 b) 2Mr`r^2 C) both a and b Lecture 6 1. For which force the inverse square law force has +ve value of k: a) Repulsive force. b) b) Attraction force. c) c) Both. d) d) Nothing 2. What is the general equation of the conic with one focus on the origin a) 1/r= C[1+€cos(0 - 00)] b) 1/r= C[1+€sin(0 - 00)] c) 1/r= C[1-€cos(0 + 00)] d) 1/r= C[1+€tan(0 - 00)] 3. The nature of the orbit is an ellipse when the eccentricity is: a) €>1 b) €=1 c) 01 d) €=0 4. In Kepler's laws, planets move in elliptical orbit with the sun at one focus is called: a) Law of area b) Last of period c) Law of orbit d) none of these 5. The number of particles crossing a unit area placed normal to the beam in a unit time called: a) flux density b) normal velocity c) acceleration 10 | P a g e Downloaded by RASAL SANSKRUTI ([email protected])  lOMoARcPSD|48187727 Multiple Choice Questions Classical Mechanics BS Mathematics(2017-2021) d) none of them 6. When a particle approaches a centre of force, it will a) Attracted b) Repelled. c) either be attracted or repelled d) neither attracted nor repelled 7) The impact parameter is defined by the distance that is between the centre of force and the incident velocity direction is: a) Perpendicular b) Parallel c) Tangent d) all of these 8) The assumption that no incident particle interacts with more than one target nucleus of valid if: a) scattering angle not too small b) scattering angle not too big. c) scattering angle absolute zero d) scattering angle is zero Moo repulsive force if: a) ZZ' e b) ZZ' e2 c) ZZ' e3 d) ZZ' e4 10) In which case of force k has the -ve value of repulsive force: a) Gravitational force b) Coulomb force c) Both d) Neither 11) How many constants of the four constants of integration appear in the orbit equation: a) 1 b) 2 c) 3 d) 4 11 | P a g e Downloaded by RASAL SANSKRUTI ([email protected])  lOMoARcPSD|48187727 Multiple Choice Questions Classical Mechanics BS Mathematics(2017-2021) 12) The nature of orbit depends on : a) Radius b) Eccentricity c) Origin d) Angle 13) In the equation of the orbit, position corresponding to r=r min is a) Percenter b) Apo centre c) Perihelion d) Aphelion 14) The orbital eccentricities of the planets vary from a) 0.07 to 0.249 b) 0.007 to 0.0249 c) 0.007 to 0.249 d) 0.7 to 0.249 15) Halley's comet has a value of eccentricity : a) 0.967 b) 0.0967 c) 0.9 d) 1.067 16) Angle between the incident and scattered direction is said to be a) solid angle b) scattering angle c) origin angle d) eccentricity 17) On approximate expression T2=4π2a3/Gm2 , the proportionality constant for all planet's is :. a) zero b) remain same c) +ve d) -ve Lecture 7 12 | P a g e Downloaded by RASAL SANSKRUTI ([email protected])  lOMoARcPSD|48187727 Multiple Choice Questions Classical Mechanics BS Mathematics(2017-2021) Qno1: The laboratory coordinate system is in the one where scatterer is at rest and incident parties _____. a) Scatter b) b)initial direction c)finial direction d) rest Qno2: The scattering in laboratory coordinate system are made _____. a) Initiator b) actual measurements c)scattering angle d)all of above Qno3: The scattering angle measured in laboratory coordinates is angle between _____ of the scattered particle. a)Account initial and finial directions b) opposition c) rest d) none of these Qno4: The scattering angle calculated from _____ one body problem. a) Center b) equivalent. c) unequal. d) both a and c Qno5: r1 and v1 is the position and velocity after scattering of the_____ in the laboratory system. a)initial particle b) finial particle c) incident particle d) all of above Qno6: R and V is the position and velocity of the _____ in the laboratory system. a) Ceter of mass b) b) center of gravity c) c) incident particle d) d) all of above Qno7: If the scattering is inelastic then 13 | P a g e Downloaded by RASAL SANSKRUTI ([email protected])  lOMoARcPSD|48187727 Multiple Choice Questions Classical Mechanics BS Mathematics(2017-2021) a) V=Vo b) b)V not equal to Vo c) V>V1 d) d) all of these Qno8: The scatterer is initial at rest so according to law of conservation ___. a) Linear momentum b) angular momentum C) both a and b d) none of these Qno9: which is true equation ? a) (m1+m2)=m1vo b) b) (m1+ m)>vo c) c) (m1+m2)v=m1vo d) d) mi>mv Qno10: The scattering angle in the laboratory coordinate system is___. a)Tan(x)= AB/BA b)Tan(y)=BA/AB C)both a and b d) Tan(x) =AB/OB Qno11: If collision is elastic then a) V= Vo b) b) p=m1/m2 c) c) both a and b d) d) all of above Qno12: Solid angle but be same in the a)center of a)mass b) laboratory coordinate system c) both a and b d) all of above Qno13: when the scattering is elastic collision then. a) m2>m2 b) b) m11 (c) 0< ε >1 (d) 0> ε