System Of Particles And Rotational Motion Mock Test

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Quiz: System of Particles and Rotational Motion – Progressive Test
Total questions: 480
Questions in this round: 50
Time allotted: 70 minutes
Pass score: 60%
Total rounds: 10
Current round: 1^st
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Quiz: System of Particles and Rotational Motion – Certificate Challenge
Total questions: 480
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Certificate pass score: 70%
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Progressive Test — Guest First Round

System of Particles and Rotational Motion – Progressive Test

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1 / 50

1. A compact summary of pure rolling is shown below. Select the unsuitable row.

Row	Quantity or condition	Correct statement
P	Contact point speed	Zero instantaneously relative to ground
Q	Speed relation
R	Total kinetic energy
S	Slipping condition	must still hold exactly

a) Row R

b) Row S

c) Row P

d) Row Q

2 / 50

2. A body rolls without slipping from rest down a height . If its value of in is , the speed formula reduces to

3 / 50

3. A graph compares acceleration down the same incline for rolling bodies with different values of , where . As increases, the graph should show

a) becoming independent of body shape

b) , so it decreases

c) remaining equal to

d) , so it increases

4 / 50

4. If the angular speed of a rigid body rotating about a fixed axis is doubled while its moment of inertia remains unchanged, its rotational kinetic energy becomes

a) half the original value

b) three times the original value

c) twice the original value

d) four times the original value

5 / 50

5. Match the type of continuous distribution with a suitable mass element idea.

Column I	Column II
P. Thin wire	1. Line mass element
Q. Thin lamina	2. Area mass element
R. Solid body	3. Volume mass element
S. Whole body mass	4.

a) P-4, Q-2, R-3, S-1

b) P-1, Q-2, R-3, S-4

c) P-1, Q-3, R-2, S-4

d) P-2, Q-1, R-3, S-4

6 / 50

6. Angular momentum of a particle about a point is defined as

7 / 50

7. A rigid body is best idealised as a body in which

a) every particle remains fixed at one position

b) distances between particle pairs remain fixed

c) the body has zero mass and zero size

d) all particles move only along straight paths

8 / 50

8. A system has constant total momentum . Its centre of mass must

a) move with steadily increasing acceleration

b) remain permanently at rest at the origin

c) move with constant velocity

d) move automatically in a circular path

9 / 50

9. Two carts on a smooth horizontal track are initially at rest with a compressed spring between them. After release, the cart moves left with speed . The speed of the cart is

a) to the right

b) to the right

c) to the right

d) to the right

10 / 50

10. Use the graph description below.

A graph of net torque versus time for a rotating body lies above the time axis. The shaded area under the graph from to is .

The shaded area represents

a) rotational kinetic energy directly

b) change in angular momentum

c) moment of inertia

d) angular displacement

11 / 50

11. A force of acts at a distance from a pivot, and the force is perpendicular to the position vector from the pivot. The torque magnitude is

12 / 50

12. Match the situation with the suitable system-choice caution.

Column I	Column II
P. Explosion into fragments	1. Include all fragments for total momentum conservation
Q. Rocket ejecting fuel	2. Decide whether ejected fuel is part of the system
R. Two carts pushing apart	3. Spring forces are internal if both carts are included
S. Single cart chosen alone	4. Contact or string force from outside may be external

a) P-4, Q-2, R-3, S-1

b) P-2, Q-1, R-3, S-4

c) P-1, Q-3, R-2, S-4

d) P-1, Q-2, R-3, S-4

13 / 50

13. A solid sphere rolls without slipping down an incline. The minimum coefficient of static friction needed for pure rolling is found by comparing the required friction with the normal reaction. If , then the required friction is

14 / 50

14. Consider the following statements about conservation of linear momentum.
I. It applies to a chosen system when the net external force is zero.
II. It can apply even when strong internal forces act.
III. It requires the centre of mass to be at rest in every inertial frame.

a) I, II, and III

b) I and II only

c) II and III only

d) I and III only

15 / 50

15. Two unequal masses are placed at the ends of a light rod of length . If is at the left end and is at the right end with , the centre of mass lies

a) outside the rod beyond the left end

b) exactly at the midpoint of the rod

c) between the midpoint and the right end

d) between the left end and the midpoint

16 / 50

16. A compound wheel has two coaxial parts. A force acts tangentially at radius , while another equal force acts tangentially in the opposite rotational sense at radius . The net torque magnitude is

17 / 50

17. For a composite body made of simple parts, the centre of mass can often be found by

a) using only the outermost dimensions of the body

b) placing it at the geometrical centre in every case

c) ignoring the masses of larger parts of the composite body

d) treating each part as concentrated at its centre of mass

18 / 50

18. A particle moves in a circle about the origin under a force directed toward the origin. Its angular momentum about the origin is conserved because

a) the torque about the origin is zero

b) the force is always perpendicular to the radius

c) the particle has no linear momentum

d) the speed must remain zero

19 / 50

19. A solid sphere of mass and radius rolls without slipping on a rough horizontal surface. A horizontal force of acts through its centre towards the right, and an external couple of acts clockwise. If , what is the acceleration of the centre and the direction of friction?

a) , friction towards the left

b) , friction towards the left

c) , friction

d) , friction towards the right

20 / 50

20. Take as east, as north, and as upward. A vector points north and a vector points east. The direction of is

a) downward, along

b) northward, along

c) east, along

d) upward, along

21 / 50

21. A solid cylinder rolling without slipping has total kinetic energy . The ratio of its translational kinetic energy to rotational kinetic energy is

22 / 50

22. In the negative-mass method for a lamina with a hole, the removed part is treated as

a) zero mass placed only at the chosen origin

b) a positive mass at the centre of mass of the removed part

c) a negative mass at the removed part's centre of mass

d) a force acting at the edge of the hole

23 / 50

23. For a uniform thin rod along the -axis, the small mass element may be written as , where is constant. This helps because

a) it removes the need to locate the rod

b) it changes the rod into a point particle

c) it relates each mass element to a length element

d) it makes the total mass of the rod equal to zero

24 / 50

24. In the integral , the vector represents

a) the torque vector on each mass element

b) the angular velocity vector of the body

c) the position vector of each small mass element

d) the radius measured only from the outer surface

25 / 50

25. A uniform square lamina of side has a small square of side removed from one corner. To set up the centre-of-mass calculation using the subtraction method, the correct idea is to use

a) only the outer boundary of the remaining shape

b) the removed square as positive mass and the full square as negative mass

c) the geometrical centre of the original square without any correction

d) the full square as positive mass and the removed square as negative mass

26 / 50

26. In the vector formula , shifting every particle by the same displacement vector changes the centre-of-mass position vector by

27 / 50

27. A solid cylinder of mass and radius rests on a rough horizontal floor. A light string is wound around the cylinder and pulled horizontally towards the right from the topmost point with a force of . The cylinder rolls without slipping. If and , find the acceleration of the centre and the minimum coefficient of static friction required.

a) ,

b) ,

c) ,

d) ,

28 / 50

28. In a uniform metre scale balanced at its centre, the weight of the scale itself produces no torque about the support because

a) gravity cannot produce torque about any support

b) its weight passes through the support point

c) the support force is always zero

d) the scale has zero mass

29 / 50

29. A rolling body of mass descends height without slipping. If its speed at the bottom is , the total kinetic energy at the bottom is

a) only

b) only

c) zero because static friction acts

30 / 50

30. Assertion: The centre of mass of a uniform ring lies at its geometrical centre.
Reason: The material of a uniform ring is concentrated at the geometrical centre.

a) Both Assertion and Reason are true, and Reason explains Assertion

b) Both Assertion and Reason are true, but Reason does not explain Assertion

c) Assertion is false, but Reason is true

d) Assertion is true, but Reason is false

31 / 50

31. In applying the right-hand rule for , the fingers of the right hand are curled from

a) toward , and the thumb gives

b) the thumb toward the palm, and the fingers give

c) toward , and the thumb gives

d) toward , and the thumb gives

32 / 50

32. Pure rolling without slipping of a wheel on a horizontal surface requires the contact point to have

a) zero angular speed relative to the ground

b) speed upward relative to the ground

c) zero ground velocity at that instant

d) speed relative to the ground

33 / 50

33. A rigid body rolls without slipping down an incline of angle . If its moment of inertia about the centre of mass is , the acceleration of its centre of mass is

34 / 50

34. Two particles of masses and are separated by a distance . Measured from the particle of mass , the distance of the centre of mass is

35 / 50

35. In the component method for a many-particle system, is found using

a) the mass-weighted average of all -coordinates

b) the simple average of all distances from the origin

c) only the particles lying on the -axis

d) only the largest -coordinate

36 / 50

36. Consider the following statements about centre of mass by symmetry.
I. A uniform solid sphere has its centre of mass at its centre.
II. A uniform circular disc has its centre of mass at its centre.
III. A uniform ring cannot have its centre of mass at an empty point.

a) I, II, and III

b) II and III only

c) I and III only

d) I and II only

37 / 50

37. Use the graph description below.

For bodies rolling without slipping from the same height , a graph is plotted between at the bottom and , where .

The slope of this graph is

38 / 50

38. In the notation used for rotational motion, is introduced as the symbol for

a) moment of inertia

b) centre-of-mass velocity

c) angular displacement

d) linear momentum

39 / 50

39. Study the table and identify the row that contains a wrong conclusion for two particles on a line.

Row	Condition	Conclusion
P		is at the midpoint
Q		lies closer to
R	Both masses are positive	lies between the two particle positions
S	Origin is shifted	The physical location of the centre of mass changes

a) Row S

b) Row P

c) Row Q

d) Row R

40 / 50

40. In the expression , if is resolved into a component parallel to and a component perpendicular to , only the perpendicular component contributes because

a) the parallel component gives

b) the parallel component is always larger

c) cross product ignores all components

d) the perpendicular component has zero magnitude

41 / 50

41. Internal torques in a system of particles cancel in the total angular momentum equation when the internal forces are central because

a) each force pair acts along the joining line

b) angular momentum is not a vector quantity

c) each internal force has zero magnitude

d) the interacting particles have equal masses

42 / 50

42. A rotating wheel has constant angular speed. A point on its rim has

a) zero tangential acceleration but non-zero centripetal acceleration

b) only angular acceleration and no linear acceleration

c) both accelerations zero

d) non-zero tangential acceleration but zero centripetal acceleration

43 / 50

43. A rigid body has , but about its centre of mass. The body can

a) have translational acceleration without angular acceleration

b) have neither rotation nor translation possible

c) have angular acceleration without translational acceleration

d) remain in complete equilibrium

44 / 50

44. A leaking cart moves on a smooth horizontal track while sand falls vertically out of it. If the chosen system is "cart plus the sand that has not yet fallen out," the system mass

a) equals only the mass of fallen sand

b) decreases with time

c) becomes negative

d) remains fixed automatically

45 / 50

45. Study the table and choose the row that correctly describes the quantity in .

Row	Meaning of
P	Perpendicular distance of the particle from the axis
Q	Distance travelled by the particle in time
R	Distance of the particle along the axis
S	Distance of the centre of mass from any chosen origin only

a) Row Q

b) Row S

c) Row P

d) Row R

46 / 50

46. A solid cylinder of mass and radius lies on a rough horizontal surface. A horizontal force of is applied through its centre towards the right. The cylinder rolls without slipping. If , what are the acceleration of its centre and the direction of static friction?

a) , with friction towards the right

b) , with zero friction

c) , with friction towards the left

d) , with friction towards the left

47 / 50

47. Study the table for three particles and choose the expression that correctly gives .

Particle	Mass	-coordinate
P
Q
R

48 / 50

48. Particles of masses and are placed at and . A third particle of mass is placed at . If the centre of mass is at , the value of is

49 / 50

49. The centre of gravity of a body is the point through which

a) the whole weight may be considered to act

b) the whole mass is physically concentrated

c) the body must be supported from below

d) all external forces must pass

50 / 50

50. Study the table and identify the row that misuses conservation of linear momentum.

Row	Situation	Conclusion
P	Two carts push apart on a smooth track	Total horizontal momentum remains constant
Q	Fragments of a shell during a very short explosion	Internal forces may change individual momenta
R	A ball falling freely under gravity	Vertical momentum of the ball alone is conserved
S	Two balls collide on a smooth table	Total horizontal momentum is approximately conserved

a) Row S

b) Row R

c) Row Q

d) Row P

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System of Particles and Rotational Motion Mock Test – Class 11 Physics

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System of Particles and Rotational Motion – Progressive Test

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