FBQ1: A vector a is a _______________ specified by a magnitude and direction in space. Answer: Quantity FBQ2: The vector a may be represented geometrically by an arrow of length α drawn from any point in the appropriate _______________. Answer: Direction FBQ3: Any vector can be specified, with respect to a given set of Cartesian axes, _______________. Answer: three component FBQ4: If X.YZ are the Cartesian co-ordinates of P, then we write ______________, and say the X, Y, Z are the components of r. Answer: r= (X, Y, Z) FBQ5: _______________of two vectors a and b may be defined geometrically by drawing one vector from the head of the other. Answer: Addition FBQ6: Any vector r can be written as a sum of three _____________along the three axes. Answer: Vectors FBQ7: If _____________is the angle between the vectors a and b, then by elementary trigonometry the length of their sum is given [a + b] = a + b + 2abcos⁡θ. Answer: Theta FBQ8: The scalar products of the ___________ i, j, k are i2=j2=k2=1,  i.j=j.k=k.i=0. Answer: 1 FBQ9: If we take the ____________ of two vectors a and b, we find a.b = axbx+ayby+azbz, and in particular r2=X2+Y2+Z2.  Answer: scalar product FBQ10: A vector whose sense is merely conventional, and would be reversed by changing from a right – hand to a left – hand convention is called an ____________, as opposed to an ordinary or polar vector. Answer: axial vector FBQ11: The vector product of two ____________ is thus an axial vector. Answer: Polar vector FBQ12: From any three vectors a,b,c we can form the ___________ (a^b).c. Answer: scalar triple vectors FBQ13: The vector distance travelled by the particle in a ___________ ∆t is ∆r=rt+∆t-rt. Answer: short time interval FBQ14: The velocity, or derivative with respect to t, is defined just as for scalars, as the ______________, r = drdt = lim∆t→0⁡∆r∆t. Answer: Limit FBQ15: The rate of change of the distance r from the origin is equal to the _____________of the velocity vector. Answer: Radial component FBQ16: A scalar field is a _______________ ∅(X,Y,Z) of position in space. Answer: Scalar function FBQ17: If the distance |dr| is fixed, then this scalar product takes on its ____________ when dr is in the direction of V∅. Answer: Maximum value FBQ18: The symbol ∇ may be regarded as a vector which is also a ______________ given by ∇ =i∂∂x+j∂∂y+k∂∂z. Answer: Differential operator FBQ19: The _____________ is defined to be DivA = ∇.A=∂Ax∂xi+∂Ay∂yj+∂AZ∂zk. Answer: Divergence of A FBQ20: ∇ ^A= ijk∂∂x∂∂y∂∂zAxAyAz is called _______________. Answer: Curl of A FBQ21: An important identity, analogous to the expansion of the ____________ is ∇ ^ (∇ ^A)= ∇∇.A-∇2A. Answer: Vector triple product FBQ22: There are three important theorems for vectors which are generalizations of the _______________ of the calculus,    ∫x0x1dfdxdx=fx1-f(x0). Answer: Fundamental theorem FBQ23: _______________ states that if A is any vector field, then Answer: Stoke’s theorem FBQ24: ______________ states that if V is a volume in space bounded by the closed surface S, then for any vector field B, ∭dv∇∙B=∬sds∙B . Answer: Gausss’s theorem FBQ25: The speed V of a particle is defined to be the _____________ of distance (along the path) with respect to time. Answer: Rate of change FBQ26: One of the uses of the ________________ is to provide expressions for the gradient, divergence and curl in terms of curvilinear co – ordinates. Answer: Integral theorem FBQ27: To find an expression for the divergence, we use ______________, applied to a small volume bounded by the coordinate surface. Answer: Gauss’s theorem FBQ28: Any two _________________ vectors a and b drawn from O define a unique axis through O perpendicular to the plane containing a and b. Answer: Non-parallel FBQ29: The basic equations of ______________ are Maxwell’s equations. Answer: Electromagnetic theory FBQ30: The basic set of equations is completed by the ______________, which determines the force on a particle of charge q moving with velocity V, F = q(E + 1c V ^ B). Answer: Lorentz fore equation FBQ31: For the static case, in which all the fields are time independent; ____________, separate into a pair of electro static equations, ∇ ^ E=0, ∇.E=  4πρ, ε0-1ρ. Answer: Maxwell’s equation FBQ32: Scalars and vectors are the first two members of a family of quantities known as _______________. Answer: Tensors FBQ33: Tensors are commonly denoted by sans – serif capitals like ____________ Answer: T FBQ34: For any tensor T, we define the _____________ if Tji=-Tij. Answer: Transposed tensor FBQ35: The tensor T is called _____________ if Tji=Tij. Answer: Symmetric FBQ36: T is called ____________ (or skew – symmetric) if Tji=-Tij. Answer: Antisymmetric FBQ37: The tensor R = αS+BT is the tensor with ______________ Rij=αSij+ βTij Answer: Components FBQ38: A ____________ a is called an eigen – vector of T if Ta = where is a number called eigenvalue. Answer: Vector FBQ39: If ∇M is the total mass of a volume ∆T of particles, then the ____________ can be defined as δ= lim∆T→0⁡∆M∆T Answer: Density FBQ40: The density is a ________ and can vary from point to point. Answer: Function of position FBQ41: When the density is a ___________, the systems is said to be of uniform density or simply uniform. Answer: Constant FBQ42: When the continuous system of particles occupy a surface, we can similarly define a ___________ or mass per unit area. Answer: Surface density FBQ43: In practice, force applied to systems of particles will change the ____________ between individual particles, such system are often called deformable or ___________. Answer: Distance, elastic body FBQ44: The distance between any two specified particles of a system remains the same regardless of _________ such a system is called a ____________. Answer: Applied forces, rigid body FBQ45: The number of coordinates required to specify the position of a system of one or more particles is called the _____________ of the system. Answer: Degree of freedom FBQ46: The centre of mass or _________ of the system of particles is defined as that point c having position vector. Answer: Centroid FBQ47: In practice, it is fairly simple to go from discrete to continuous system by merely replacing ___________ by integrations. Answer: Summations FBQ48: If a system of particles is in a uniform _____________ the center of mass is sometimes called the center of gravity. Answer: Gravitational field FBQ49: If VV= drvdt= v is the velocity of mv, the total _____________ of the system is defined as p = ∑V=1NMVVV = ∑V=1NMVV Answer: Momentum FBQ50: If the resultant external force acting on a system of particles is ____________ then the total momentum remains constant, i.e is conserved. Answer: Zero MCQ1: For continuous systems of particles occupying a region of space it is often convenient to define a mass per unit volume which is called the Answer: Volume density MCQ2: Mathematically, if ∆M is the total mass of a volume ∆T of particles, then the density can be defined as Answer: = lim∆T →0⁡∆M ∆T  MCQ3: Density is a function of position and can vary from point to point, when the density is a constant, the system is said to be of Answer: Uniform density MCQ4: In practice, forces applied to systems of particles will change the distance between individual particles, such systems are often called Answer: Deformable bodies MCQ5: A mathematical model in which the distance between any two specified particles of a system remains the same regardless of applied forces, such a system is called a Answer: Rigid body MCQ6: The number of coordinates required to specify the position of a system of one or more particles called the Answer: Number of degrees of freedom of the system MCQ7: A particle moving freely in space requires 3 coordinates to specify its position. Thus the number of degrees of freedom is Answer: 3 MCQ8: A system consisting of N particles moving freely in space requires 3N coordinates to specify its position, thus the number of degrees of freedom is Answer: 3N MCQ9: A rigid body which can move freely in space has 6 degrees of freedom. How many coordinates are required to specify the position. Answer: 6 MCQ10: In practice, it is fairly simple to go from discrete to continuous systems by merely replacing summations by Answer: Integrations MCQ11: If a system of particles is in a uniform gravitational field, the center of mass is sometimes called the Answer: Center of gravity MCQ12: If vr= drvdt= rv is the velocity of mv, the total momentum of the system is Answer: P = ∑v=1Nmvvv= ∑v=1Nmvrv   MCQ13: Suppose that the internal forces between any two particles of the system obey Newton’s third law, then if F is the resultant external forces acting on the system, we have Answer: F = dpdt= Md2dt2 = Mddt  MCQ14: Let F = dpdt= Md2dt2 = Mddt, then putting F = 0, we find that Answer: P = ∑v=1Nmvvv= constant MCQ15: If the resultant external force acting on a system of particles is zero, then the momentum remains Answer: Constant MCQ16: If the resultant external force acting on a system of particles is zero, then the total momentum remains constant i.e is conserved. This theorem is often called Answer: Principles of conservation of momentum MCQ17: The quantity Ω = ∑V=1N(rv×vv) is called the Answer: Total angular momentum of the system of particle about origin O  MCQ18: If Fv is the external force acting on particles V, then vv× Fv is called the Answer: Moment of the force Fv MCQ19: The total external torque on a system of particles is equal to the time rate of change of the angular momentum of the system, provided Answer: The internal forces between particles are central forces MCQ20:  If both the external and internal forces for a system of particles are conservative, the Answer: Principle of conservation of energy is valid MCQ21: If the external forces are conservation, then we have Answer: Fv = -∆Vv MCQ22: The total kinetic energy of a system of particles is defined as Answer: T = 12∑v=1NMvvv2 = 12∑v=1NMvrv2 MCQ23: If Fv is the force (external or internal) acting on particle V, then the total work done in moving the system of particles is Answer: W12= ∑V=1N∫12Fvdrv MCQ24: The total work done in moving a system of particles from one state where the kinetic energy T1to another where the kinetic energy is T2, is Answer: W12 = T2- T1 MCQ25: If T and V are respectively the Total kinetic energy and total potential energy of a system of particles, then  Answer: T + V = Constant MCQ26: The total linear momentum of a system of particles about the center of mass is zero. In symbols, Answer: ∑v=1NMvvv1 = ∑v=1NMvrv.=0 MCQ27: If F is the total external force acting on a system of particles, then ∫t1t2Fdt is called the Answer: Total linear impulse MCQ28: The total linear impulse is equal to the change in linear momentum, similarly if ⋀ is the total external torque applied to a system of particles about o, then ∫t1t2⋀dt is called the Answer: Total angular impulse MCQ29: The total angular impulse is equal to the change in angular Answer: Momentum MCQ30: The limitations on the motion are often called Answer: Constraints MCQ31: If the constraints conditions can be expressed as an equation ∅(r1,r2, …, rN)=0 connecting the position vectors of the particles and the time, then the constants is called Answer: Holonomic MCQ32: If the constraints condition cannot be so expressed it is called Answer: Non – holonomic MCQ33: In order for a system of particles to be in equilibrium, the resultant force acting on each particle must Answer: Zero MCQ34: A system of particle is in equilibrium if and only if the total virtual work of the actual forces is zero i.e if ∑v=1NFv(a).δrv = 0. This is often called Answer: The principle of virtual work MCQ35: The resultants for equilibrium of a particle in a conservative force field can be generalized to Answer: Minimum MCQ36: The resultants for equilibrium of a particle in a conservative force field can be generalized to Answer: System of particles MCQ37: The other cases of equilibrium where the potential is not a minimum are called Answer: Unstable MCQ38: A system of particles moves in such a way that the total virtual work ∑v=1N(Fva- v).δrv = 0, is often called Answer: D’ Alembert’s principle MCQ39: If V is the total potential of a system of particles depending on coordinates q1, q2, …, then the system will be in equilibrium if Answer: δVδq1=0, dVδq2=0, … MCQ40: The simple pendulum is one of the most common examples of Answer: Simple harmonic motion MCQ41: A harmonic motion is one for which the restoring force obeys Answer: Hooke’s law MCQ42: Vibrating and periodic motion is a prototype of the motions of most Answer: Physical system MCQ43: The angular equation of motion of a pendulum is simply Answer: MCQ44: Which of the following is not part of the three basic notions for analyzing motion? Answer: Position MCQ45: The displacement vector ∆r=rt+ ∆t-r(t) represents the Answer: Change in position MCQ46: The scalar ∆r/∆t represents the average change in position from time t to  Answer: t + ∆t MCQ47: The average change in position is called Answer: The average velocity over the time period ∆t MCQ48: Velocity is the rate of change of position with respect to Answer: Time MCQ49: The rate of change of velocity with respect to time is called the Answer: Acceleration MCQ50: The speed V of a particle is defined to be rate of change of distance with respect to Answer: Time