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1. The position vectors of masses 2kg, 3kg and 4kg are respectively 2 i – 3 j , i + j + k and 4 j + 3 k . The position of the centre
of mass is

2. I. the transformation equations in 2-D polar co-ordinates are   ; y = rsin ( )

Where,
II. The transformation equations in 3-D spherical polar co-ordinates are x  r sincos ; y = rsinsin ; z = rcos
Where, r (0,) ; (0,2) (0,2)
III. The transformation equations in 3-D cylindrical polar co-ordinates are;
Where,  (,) ;(0,2)

3. Identify the correct statement: ( )
(a) The linear momentum of a system of particles in general depends on the origin of frame of reference and is independent of the origin and is also zero if the frame of reference is at rest w.r.t the centre of mass.
(b) The angular momentum of a system of particles in general depends on the reference point and is independent of the reference point if and only if the reference point is at rest w.r.t the centre of mass.
(c) The kinetic energy of a system of particles in general depends on the frame of reference and is independent of the frame of reference if and only if the frame of reference is at rest w.r.t the centre of mass.
(d) All the above are correct.

4. The linear momentum of a system of particles is conserved if and only if ( )
(a) the internal forces of the system must obey weak law of action and reaction
(b) the internal forces of the system must obey weak law of action and reaction and also the external force acting on the system is zero.
(c) the internal forces of the system must obey strong law of action and reaction
(d) both (b) and (c).

5. If the total Torque acting on a particle is zero, then the conserved quantity of the particle is ( )

6. 25. I. The unit vectors, form a right handed triad in Cartesian co-ordinate system. ( )
II. The unit vectors form a right handed orthogonal triad in spherical polar co-ordinate system.
III. The unit vectors form a right handed triad in cylindrical co-ordinate system.
(a)I,II and III are correct (b) I is correct (c) II is correct (d) III is correct.

7. I. the internal forces of the system must obey strong law of action and reaction and each of them must be a conserved force.
II. the internal forces of the system must obey weak law of action and reaction.
III. Each of the external force acting on the system must be a conserved force.
The total energy ( P.E + K.E) of a system of particles is conserved in an inertial frame if and only if ( )

8. If the internal forces in the above system are Gravitational forces, then the total external force acting on the system at t = 3sec in Newton is

9. Newton’s laws of motion are valid in

10. Identify the correct statements. ( )
(a) The SI units of linear momentum, angular momentum and Torque are kgms-1, kgm2s-1,Nm.
(b) The rate of change of angular momentum of a system of particles is always to the external torque acting on the system i.e.,
dL/dt = external torque
(c) The conservation theorms of linear momentum, angular momentum and total energy of a system of particles are valid in both inertial and
Non-inertial frames.
(d) all the above.

11. Identify the Correct Statements : ( )
(a) The linear momentum of a system of particles is equal to the total mass of the system times the velocity of the centre of mass.
(b) The angular momentum about a point ‘o’ is equal to the angular momentum of motion concentrated at the centre of mass, plus the
angular momentum of the motion about the centre of mass.
(c) The kinetic energy of a system of particles in general depends on the frame of reference and is independent of the frame of reference
if and only if the frame of reference is at rest w.r.t the centre of mass.
(d) All the above are correct.

12. Particles of masses 4, 3 and 1kg move under a force such that their position vectors at time ‘t’ are
r1 = 3 j + 2 t^2 k ; r2 = 3t i – k and r1 = 4t i + t^2 j . The velocity of the centre of mass at t = 1sec is

13. Newton’s III law is not valid for ( )

14. A force F is said to be a conservative force if and only if ( )

15. I. Weak law of action and reaction means that the action and reaction forces must be equal and opposite. ( )
II. Strong law of action and reaction means that both the action and reaction forces must act along the line joining the particles exerting forces on each other. The action and reaction forces need not equal and opposite.
III. Strong law of action of reaction means that in addition to being equal and opposite, they must act along the line joining the particles exerting forces on each other.

16. A particle of mass ‘m’ is at rest at the origin of the co-ordinate system. At t = 0, a force ‘bt’ starts acting on the particle. Then, the velocity and
the position of the particle are given by, ( )

17. If the total force acting on a particle is zero, then the conserved quantity of the particle is ( )

18. A particle of unit mass is falling under the action of gravity near the Earth’s surface. If the force due to the friction of the air is directly proportional
to its instantaneous velocity, the velocity and position of the particle are given by,

19. The Kinetic Energy of the above system at t = 1sec in Joule is ( )

20. In Newton’s III law, the Action and Reaction forces act on

21. If the force acting on a particle is a conservative force, then the conserved quantity of the particle is ( )

22. Identify the correct statement :

(a) F = (ax + by^2 )i + (az+2bxy)j + (ay+bz )k is a conservative force ( a and b are constants)
(b) F = A x r ; (A is a constant vector) is a conservative force.
(c) both (a) and (b) are true
(d) none of the above.

23. The position vectors of masses 2kg, 3kg and 4kg are respectively 2 i – 3 j , i + j + k and 4 j + 3 k . The position of the centre
of mass is

24. The angular momentum of a system of particles w.r.t an origin fixed to an inertial frame of reference is conserved if and only if ( )
(a) the internal forcesof the system must obey weak law of action of reaction.
( b) the internal forcesof the system must obey weak law of action and reaction and also the external torque acting on the system is zero.
(c) the internal forcesof the system must obey strong law of action and reaction and also the external Torque acting on the system is zero.