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Ans:
Here A=(A^X₂+A^Y₂+A^Z₂)^1/2
OR                 A= [(5)²+(0)²+(5)²]^1/2=5 (2)^1/2
Now     Cos =Ax/A= 5/5( 2)^1/2=1/(2)^1/2 or = 45^o WITH X-axis
             Cos =Ay/a=0/5 (2)^1/2=0 or = 90^o with Y-axis
and        Cos =Az/a=5/5 (2)^1/2 =1/(2)^1/2 or y=45^o with Z-axis

Ans:
According to Newton's first law every body remains in a state of rest or of uniform motion in a straight line unless it is compelled by some external force to change that state.
Definition of force from Newton's first law : According to Newton's first law, a body remains in state of rest or of uniform motion unless some force is applied to change its state i.e, if there is no force applied, there will be no change in state of rest or of uniform motion of a body. This means force is that which produces a change in state of rest or of uniform motion. If the force is that which produces a change, it may only try to do so. Hence force is that which produces or tries to produce a change in state of rest or of uniform.

Ans:
Energy of a body is its capacity of doing work. Its units and dimensions are same as those of work. Its units are joule,erg,g cm and kg m. Its dimensions is [ML²T^-2].
Energy is of several types, mechanical, heat, sound, light, magnetic, electric, atomic, nuclear, chemical, solar energy and so on .
Mechanical energy is of two types, kinetic and potential energy.

Ans:
Centre of mass of a system is the point at which the entire mass of the system can be supposed to be concentrated. The nature of motion of the system shall remain unaffected if all the forces acting on the system were applied directly on the centre of mass of the system.
Let m1 and m2 be situated at position vectors^->r₁ and ^->r₂ with respect to origin O. Then the centre of mass is point which will have a position vector R
defined as R=m₁^->r₁+m₂^->r₂/m₁+m₂

Ans:
Newton's law of gravitation states that very body in this universe attracts every other body with a force which is directly proportional to the product of the masses and inversely proportional to the square of the distances between them,
If m1,m2 are the two masses distance r apart, then
                      F m₁m₂/r²
                      F=Gm₁m₂/r²
where G is a constant called universal gravitational constant.
If m₁=m₂=1,r=1 then G=F
Universal gravitational constant is the force of attraction between two unit masses placed a unit distance apart.
UNIT.      G = Fr²/m₁m₂ = Nm²/kg^-2=Nm²kg^-2
DIMENSION. G =[MLT^-2][L²]/[M][M] = [M^-1L³T^-2]

Ans:
Thrust is the total normal force exerted by a liquid at rest on a given surface. it is measured in N and dyne.
Normal force excerted by liquid per unit area is called pressure or hydrostatic pressure.
P=F/A
UNIT of pressure are Pascal ( N m^-2or Pa ) in S.I. and dyn cm^-2 in cgs.

Ans:
Efficiency will decrease
                h =1-T₂/T₁=T₁-T₂/T₁Let the temperatures T₁ and T₂ be increased by x each, then
                  h'=(T_!+x)-(T₂+x)/T₁+x=T₁-T₂/T₁+x
                  h'/h=T₁/T₁+x<1[h'<h]

Ans:
Periodic motion of a body is that motion which is repeated after a fixed interval of time. The interval after which the motion is repeated is called time period.
Rotation of earth round sun ; rotation of earth around its axis and rotation of the moon around the earth are some of the examples of periodic motions.
Oscillatory motion or vibratory motion is that motion in which the body moves to and for repeatedly about a fixed point called mean position in a definite interval of time.
Motion of simple pendulum or a loaded spring or motion of liquid in a U-tube are examples of oscillatory or vibratory motion.
All vibratory motion are periodic but all periodic motions are not vibratory.

Ans:
Let OA and OB represent the velocity of 3km h ^-1 and 7km h -1 due east respectively. Let COD represent actual velocity of the wind.
Bring the man to rest by imposing upon him a velocity equal to OA'(=-OA).Impose the velocity OA' upon wind also. Since in the first case, the wind appears to come from north, the resultant of the actual velocity OD of the wind and reversed velocity i.e. OA' of the man is given by OE.
In second case, the wind appears to come from north-east. Therefore the resultant of OD and OB' (= - OB) is given by OF.
      Now ED =A'O =3km h^-1
     and     FD=B'O =7km h^-1
               FE=FD-ED= 7-3=4km h^-1
further EFO=FOE=45^o
          OE=EF=4km h^-1
Hence OD =(OE²+ED²)^1/2
                  = (4²+3²)^1/2=5km h^-1
Let      CON =0
then     tan0 =ED/OE=3/4 =0.7500
or        0=36^o,48'
Hence the wind is blowing with a velocity of 5km h ^-1 at an angle of 36 ^o48' west of north.

Ques 1. What is 1 A. U. ?
Ans: A.U. or astronomical unit is the unit of length and is equal to average distance between the sun and the earth. It is equal to 1.496 × 10¹¹m.

Ques 2. What are vector quantities ?
Ans: The physical quantities which are meaningful only if their magnitude as well as directions are given are called vectors or vector quantities. Displacement, velocity, acceleration, force, torque etc. are all vectors.

Ques 3. What is inertia ?
Ans: The inability of a body to change the position of rest or of uniform motion by itself is called inertia.

Ques 4. What is conservative force ?
Ans: A force is said to be conservative if the work done by or against the force moving a body depends upon only the initial and final positions of the body and not on the path followed. Gravitational, electrical and magnetic forces are conservative forces.

Ques 5. What is an isolated system ?
Ans: It is a system where no external force is acting.

Ques 6. What is difference between g and G ?
Ans: G is universal gravitational constant and is defined as force of attraction between two unit masses lying unit distance apart. Acceleration due to gravity is the acceleration produced in a freely falling body due to attraction of the earth.

Ques 7. What is degree of freedom ?
Ans: The number of degrees of freedom of a dynamic system is defined as the total number of co-ordinates or independent quantities required to describe completely the position and configuration of the system.

Ques 8. What is time period of a pendulum is a spaceship ?
Ans: In spaceship g = 0, therefore T = 2p(l/g)^1/2 = 2p (l/0)^1/2 = inf. Time period will be infinite and frequency will be zero.

Ques 9. What is intensity level ?
Ans: Intensity level L = log₁₀ I/I₀ Where I₀ is zero level of intensity of sound, I is the actual intensity. Its unit is decibel.

Ques 10. What is gravitational field and gravitational field intensity ?
Ans: Space around a material body in which its gravitational pull can be experienced is called its gravitational field. Intensity of gravitational field at a point due to a mass is the force experienced by a unit mass placed in the field of that mass.

Ques 12. What is particle dynamics ?
Ans: It is a branch of mechanics which deals with study of motion of objects taking into account the factors which causes motion.

Ques 16. What are significant figures? What are the rules to determine the number of significant numbers ?
Ans: Significant figures in the measured value of a physical quantity tells the number of digits in which have confidence. Larger the number of significant figures obtained in the measurement greater is the accuracy.

Ques 17. What is the speed and velocity of a particle ? Are they numerically equal ?
Ans: No,these may or may not be equal. Speed is the distance covered by a body in a unit time whereas velocity is the rate of change of displacement with time. In figure above, let a person starting from A reaches B in 0.5 hour. Speed of person = Distance/Time = 1.8/0.5 =3.6km h^-1 Velocity of person = Displacement/Time =1.2/0.5=2.4km h^-1

Ques 11. What is femto second equal to ?
Ans: It is equal to 10^-15 s.

Ques 13. What is the resultant vector?
Ans: The resultant of two or more vectors is defined as that single vector which produces the same effect as is produced by individual vector together.

Ques 14. What is linear momentum?
Ans: Momentum or linear momentum is the quantity of motion contained in the body. It is measured by the product of mass and velocity .

Ques 15. What is non-conservative force ?
Ans: A force is said to be non-conservative if the work done by or against the force in moving a body from one position to another depends upon the path followed. Friction is a non-conservative force.

Ques 18. Determine the angle which vector 5^{^}u + 0^{^}j + 5^{^}k makes with X, Y and Z axes.
Ans: Here A=(A^X₂+A^Y₂+A^Z₂)^1/2 OR A= [(5)²+(0)²+(5)²]^1/2=5 (2)^1/2 Now Cos =Ax/A= 5/5( 2)^1/2=1/(2)^1/2 or = 45^o WITH X-axis Cos =Ay/a=0/5 (2)^1/2=0 or = 90^o with Y-axis and Cos =Az/a=5/5 (2)^1/2 =1/(2)^1/2 or y=45^o with Z-axis

Ques 19. What is Newton's first law of motion ? How can we get definition of force from Newton's first law ?
Ans: According to Newton's first law every body remains in a state of rest or of uniform motion in a straight line unless it is compelled by some external force to change that state. Definition of force from Newton's first law : According to Newton's first law, a body remains in state of rest or of uniform motion unless some force is applied to change its state i.e, if there is no force applied, there will be no change in state of rest or of uniform motion of a body. This means force is that which produces a change in state of rest or of uniform motion. If the force is that which produces a change, it may only try to do so. Hence force is that which produces or tries to produce a change in state of rest or of uniform.

Ques 20. Define energy. What are its units and dimensions ?
Ans: Energy of a body is its capacity of doing work. Its units and dimensions are same as those of work. Its units are joule,erg,g cm and kg m. Its dimensions is [ML²T^-2]. Energy is of several types, mechanical, heat, sound, light, magnetic, electric, atomic, nuclear, chemical, solar energy and so on . Mechanical energy is of two types, kinetic and potential energy.

Ques 21. What is centre of mass ? Locate its position in two particle system.
Ans: Centre of mass of a system is the point at which the entire mass of the system can be supposed to be concentrated. The nature of motion of the system shall remain unaffected if all the forces acting on the system were applied directly on the centre of mass of the system. Let m1 and m2 be situated at position vectors^->r₁ and ^->r₂ with respect to origin O. Then the centre of mass is point which will have a position vector R defined as R=m₁^->r₁+m₂^->r₂/m₁+m₂

Ques 22. What is Newton's law of gravitation ? Define G. its units and dimensions.
Ans: Newton's law of gravitation states that very body in this universe attracts every other body with a force which is directly proportional to the product of the masses and inversely proportional to the square of the distances between them, If m1,m2 are the two masses distance r apart, then F m₁m₂/r² F=Gm₁m₂/r² where G is a constant called universal gravitational constant. If m₁=m₂=1,r=1 then G=F Universal gravitational constant is the force of attraction between two unit masses placed a unit distance apart. UNIT. G = Fr²/m₁m₂ = Nm²/kg^-2=Nm²kg^-2 DIMENSION. G =[MLT^-2][L²]/[M][M] = [M^-1L³T^-2]

Ques 23. What is thrust and pressure ?
Ans: Thrust is the total normal force exerted by a liquid at rest on a given surface. it is measured in N and dyne. Normal force excerted by liquid per unit area is called pressure or hydrostatic pressure. P=F/A UNIT of pressure are Pascal ( N m^-2or Pa ) in S.I. and dyn cm^-2 in cgs.

Ques 24. If temperature of source and sink are increased by the same amount, how is the efficiency of the carnot's engine affected ? Give reason.
Ans: Efficiency will decrease h =1-T₂/T₁=T₁-T₂/T₁Let the temperatures T₁ and T₂ be increased by x each, then h'=(T_!+x)-(T₂+x)/T₁+x=T₁-T₂/T₁+x h'/h=T₁/T₁+x<1[h'<h]

Ques 25. What is periodic and oscillatory motion ?
Ans: Periodic motion of a body is that motion which is repeated after a fixed interval of time. The interval after which the motion is repeated is called time period. Rotation of earth round sun ; rotation of earth around its axis and rotation of the moon around the earth are some of the examples of periodic motions. Oscillatory motion or vibratory motion is that motion in which the body moves to and for repeatedly about a fixed point called mean position in a definite interval of time. Motion of simple pendulum or a loaded spring or motion of liquid in a U-tube are examples of oscillatory or vibratory motion. All vibratory motion are periodic but all periodic motions are not vibratory.

Ques 26. To a man walking with a velocity of 3km h^-1 due east, the wind appears to blow from north but if he increases his velocity of 7km h ^-1 due east, the wind appears to blow from north east. What is the actual velocity of the wind ?
Ans: Let OA and OB represent the velocity of 3km h ^-1 and 7km h -1 due east respectively. Let COD represent actual velocity of the wind. Bring the man to rest by imposing upon him a velocity equal to OA'(=-OA).Impose the velocity OA' upon wind also. Since in the first case, the wind appears to come from north, the resultant of the actual velocity OD of the wind and reversed velocity i.e. OA' of the man is given by OE. In second case, the wind appears to come from north-east. Therefore the resultant of OD and OB' (= - OB) is given by OF. Now ED =A'O =3km h^-1 and FD=B'O =7km h^-1 FE=FD-ED= 7-3=4km h^-1 further EFO=FOE=45^o OE=EF=4km h^-1 Hence OD =(OE²+ED²)^1/2 = (4²+3²)^1/2=5km h^-1 Let CON =0 then tan0 =ED/OE=3/4 =0.7500 or 0=36^o,48' Hence the wind is blowing with a velocity of 5km h ^-1 at an angle of 36 ^o48' west of north.