p-3 : com, rotational dynamics & shmapi.coachingapis.coachinglog.in/storage/162583/vs... · 2...

1GCI

Class XIII (Spartan Batch)P-3 : COM, Rotational Dynamics & SHM

DTS (Diamond Test Series) for NEET-2020

1. The centre of mass of a body -

(1) Lies always at the geometrical centre

(2) Lies always inside the body

(3) Lies always outside the body

(4) May lie within or outside the body

2. Two particles of masses M and 2 M are at a distance D

apart. Under their mutual gravitational force they start

moving towards each other. The acceleration of their centre

of mass when they are D/2 apart is -

(1) 2GM/D2

(2) 4GM/D2

(3) 8GM/D2

(4) Zero

3. In fig a spherical part of radius R/2 is removed from a

bigger solid sphere of radius R. Assuming uniform mass

distribution, shift in the centre of mass from the centre of

main sphere will be -

(1) R

7

(2) R

14

(3)R

9

(4) R

3

4. Three masses are placed on the x–axis 300 g at origin,

500 g at x = 40 cm and 400 g at x = 70 cm. The distance of

the centre of mass from the origin is -

(1) 50 cm (2) 30 cm

(3) 40 cm (4) 45 cm

5. Moment of inertia plays the same role in rotatory motion

as in translatory motion is played by -

(1) velocity (2) acceleration

(3) mass (4) force

1.

(1)

(2)

(3)

(4)

2. M 2M D

D/2

(1) 2GM/D2

(2) 4GM/D2

(3) 8GM/D2

(4)

3. R R/2

(1) R

7

(2) R

14

(3)R

9

(4) R

3

4. x 300 g 500 g, x =

40 cm 400 g, x = 70 cm

(1) 50 cm (2) 30 cm

(3) 40 cm (4) 45 cm

5.

(1) (2)

(3) (4)

https://www.print-driver.com/?demolabel-en

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6. Three point masses, each m, are placed at the vertices of

an equilateral triangle of side 'a'. Moment of inertia of the

system about the axis COD which passes through the mass

at O and lies in the plane of triangle and perpendicular to

OA is -

(1) ma2

(2) 2

5ma2

(3) 9

4ma2

(4) 5

4ma2

7. The moment of inertia of a body does not depend on -

(1) the mass of the body

(2) the angular velocity of the body

(3) the axis of rotation of the body

(4) the distribution of the mass in the body

8. Which of the following has the smallest moment of inertia

about the central axis if all have equal mass and radii?

(1) Ring

(2) Disc

(3) Spherical shell

(4) Sphere

9. The moment of inertia of uniform circular disc of radius 'R'

and mass 'M' about an axis touching the disc at its

circumference and normal to the disc is -

(1) MR2

(2) 2

5MR2

(3) 3

2MR2

(4) 1

2MR2

6. 'a' m

COD COD,

O OA

(1) ma2

(2) 2

5ma2

(3) 9

4ma2

(4) 5

4ma2

7.

(1)

(2)

(3)

(4)

8.

(1)

(2)

(3)

(4)

9. 'R' 'M'

(1) MR2

(2) 2

5MR2

(3) 3

2MR2

(4) 1

2MR2


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10. Figure, shows a uniform rectangular sheet with BC = 2AB.

Moment of inertia of the sheet is minimum about -

(1) AB

(2) PQ

(3) RS

(4) AD

11. A circular disc X of radius R is made from an iron plane of

thickness t and another disc Y of radius 4R is made from

an iron plate of thickness t/4. Then the relation between

the moment of inertia Ix and I

y about an axis passing through

its centre and perpendicular to its plane is -

(1) Iy = 32 I

x

(2) Iy = 16 I

x

(3) Iy = I

x

(4) Iy = 64 I

x

12. A thin circular ring of mass M and radius r is rotating about

an axis passing through its centre and perpendicular to its

plane with a constant angular velocity. Two objects, each

of mass m are attached gently to the opposite ends of a

diameter of the ring. The ring now rotates with angular

velocity -

(1) M m

M m

2

2

b g

(2) M(M – m)

(3) M m

M

2b g

(4) M

M m 2

13. A uniform heavy disc is rotating at constant angular velocity

() about a vertical axis through its centre O. Some wax W

is dropped gently on the disc. The angular velocity of the

disc -

(1) does not change (2) increase

(3) decreases (4) becomes zero

10. BC = 2AB

(1) AB

(2) PQ

(3) RS

(4) AD

11. X R t

Y 4R t/4

Ix

Iy

(1) Iy = 32 I

x

(2) Iy = 16 I

x

(3) Iy = I

x

(4) Iy = 64 I

x

12. m r

m

(1) M m

M m

2

2

b g

(2) M(M – m)

(3) M m

M

2b g

(4) M

M m 2

13. O

() W

(1) (2)

(3) (4)


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14. A particle is moving along a straight line parallel to x–axis

with constant velocity. Angular momentum of particle about

the origin in vector form -

(1) mvbk (2) mvbk

(3) +mvak (4) -mvak

15. The moment of inertia of NaCI molecule with bond length r

about an axis perpendicular to the bond and passing through

the centre of mass is -

(1) m m rNa Clb g2

(2) m m

m mNa Cl

Na Cl

(3) m m

m mrNa Cl

Na Cl

2

(4) m m

m mrNa Cl

Na Cl

2

16. A smooth uniform rod of length L and mass M has identical

beads of negligible size, each of mass m, which can slide

freely along the rod. Initially the two beads are at the centre

of the rod and the system is rotating with angular velocity

0 about an axis perpendicular to the rod and passing

through the mid point of the rod., There are no external

forces. When the beads reach the ends of the rod, the

angular velocity of the rod would be -

(1) M

M m

0

2

(2) M

M m

0

4

(3) M

M m

0

6

(4) M

M m

0

8

14. x–

(1) mvbk (2) mvbk

(3) +mvak (4) -mvak

15. NaCI r

(1) m m rNa Clb g2

(2) m m

m mNa Cl

Na Cl

(3) m m

m mrNa Cl

Na Cl

2

(4) m m

m mrNa Cl

Na Cl

2

16. L M

m

0

(1) M

M m

0

2

(2) M

M m

0

4

(3) M

M m

0

6

(4) M

M m

0

8


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17. On a smooth inclined plane a body of mass M is attached

between two springs. The other ends of the spring are

fixed with rigid supports. If each spring has a force constant

k, the period of oscillation of the body is -

(assuming the spring as massless)

k

kM

(1) 22

M

k

(2) 22

M

k

(3) 22

M

k

sin

(4) 22

M

k

sin

18. Acceleration-displacement graph of a particle executing

SHM Is as shown in given figure. The time period of its

oscillation is (in sec)

a(m/s )2

x(m)45º

(1) 2

(2) 2

(3)

(4) 4

17. M

k

( )

k

kM

(1) 22

M

k

(2) 22

M

k

(3) 22

M

k

sin

(4) 22

M

k

sin

18. SHM

( )

a(m/s )2

x(m)45º

(1) 2

(2) 2

(3)

(4) 4


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19. Figure shows a flywheel of radius 10 cm. Its moment of

inertia about the rotation axis is 0.4 kg-m2. A massless

string passes over the flywheel and a mass 2 kg is attached

at its lower end. Angular acceleration of the pulley is nearly-

(1) 4.8 rad/s2

(2) 6.2 rad/s2

(3) 3.2 rad/s2

(4) 9.6 rad/s2

20. A unifrom disc of radius R is pivoted at point O on its

circumference. The time period of small oscillations about

an axis passing through O and perpendicular to plane of

disc will be -

(1) 2R

g

(2) 22

3

R

g

(3) 22

R

g

(4) 23

2

R

g

21. A particle executes SHM. Its velocities are v1 and v2 at

displacements x1 and x2 from mean position respectively.

The frequency of oscillation will be -

(1) 1

212

22

12

22

1 2

v v

x x

L

NMM

O

QPP

/

(2) 1

212

22

22

12

1 2

v v

x x

L

NMM

O

QPP

/

(3) 1

212

22

12

22

1 2

x x

v v

L

NMM

O

QPP

/

(4) 1

222

12

12

22

1 2

x x

v v

L

NMM

O

QPP

/

19. 10 cm

0.4 kg-m2

2 kg

(1) 4.8 rad/s2

(2) 6.2 rad/s2

(3) 3.2 rad/s2

(4) 9.6 rad/s2

20. R

O O

(1) 2R

g

(2) 22

3

R

g

(3) 22

R

g

(4) 23

2

R

g

21. x1 x2

v1 v2

(1) 1

212

22

12

22

1 2

v v

x x

L

NMM

O

QPP

/

(2) 1

212

22

22

12

1 2

v v

x x

L

NMM

O

QPP

/

(3) 1

212

22

12

22

1 2

x x

v v

L

NMM

O

QPP

/

(4) 1

222

12

12

22

1 2

x x

v v

L

NMM

O

QPP

/


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22. An object suspended from a spring exhibits oscillations of

period T. Now the spring is cut in two halves and the same

object is suspsended with two halves as shown in figure.

The new time period of oscillation will become -

(1) T

2

(2) 2T

(3) T

2

(4) T

2 2

23. A particle of mass m is located in a potential field given by

U(x) = U0 (1– cos ax) where U0 and a are constants. The

period of small oscillations is -

(1) 2 U

ma

02

(2) 2 mU

a

02

(3) 2 a

mU

2

0

(4) 2 m

U a02

24. The time period of a simple pendulum having infinite length

is -

(1)

(2) 2 R g/

(3) 2 2 R g/

(4) 2 2 / g

22. T

(1) T

2

(2) 2T

(3) T

2

(4) T

2 2

23. m U(x) = U0 (1- cos ax)

U0 a -

(1) 2 U

ma

02

(2) 2 mU

a

02

(3) 2 a

mU

2

0

(4) 2 m

U a02

24.

(1)

(2) 2 R g/

(3) 2 2 R g/

(4) 2 2 / g


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25. A ring or radius 3a is fixed rigidly on a table. A small ring

whose mass is m and radius a, rolls without slipping inside

it as shown in the figure. The small ring is released from

position A. When it reaches at the lowest point, the speed

of the centre of the ring at that time would be -

(1) 2ga

(2) 3ga

(3) 6ga

(4) 4ga

26. Two discs have same mass and thickness. Their materials

are of densities 1 and 2 . The ratio of their moment of

inertia about central axis will be -

(1) 1 : 2

(2) 1 2 : 1

(3) 1 : 1 2

(4) 2 : 1

27. A wheel is rolling uniformly along a level road (see figure).

The speed of transitional motion of the wheel axis is V.

What are the speeds of the points A and B on the wheel

rim relative to the road at the instant shown in the figure -

(1) VA = V ; VB = 0

(2) VA = 0; VB = V

(3) VA = 0 ; VB = 0

(4) VA = 0; VB = 2V

25. 3a

m a

(1) 2ga

(2) 3ga

(3) 6ga

(4) 4ga

26.

1 2

(1) 1 : 2

(2) 1 2 : 1

(3) 1 : 1 2

(4) 2 : 1

27.

V

A B

(1) VA = V ; VB = 0

(2) VA = 0; VB = V

(3) VA = 0 ; VB = 0

(4) VA = 0; VB = 2V


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28. A body of radius R and mass m is rolling on a horizontal

plane without slipping with speed v. It then rolls up a hill of

vertical height h. If h = 3v2/4g, the body is -

(1) Ring

(2) Cylinder

(3) Solid sphere

(4) Spherical shell

29. Angular Momentum is -

(1) a polar vector

(2) an axial vector

(3) a scalar

(4) none of these

30. A uniform solid cylinder of mass M and radius R rotates on

a horizontal, frictionless axel. Two masses hung from light

cords wrapped around the cylinder. If the system is released

from rest, the tension in each cord is -

(1) Mmg

M m( ) (2) Mmg

M m( ) 2

(3) Mmg

m m( ) 3(4)

Mmg

M m( ) 4

31. Three particles are connected by light, rigid rods lying along

the y-axis. If the system rotates about the x-axis with an

angular speed of 2rad/s, the M.I. of the system is -

(1) 46 kg-m2 (2) 92kg-m2

(3) 184 kg-m2 (4) 276 kg-m2

28. m R v

h

h = 3v2/4g

(1)

(2)

(3)

(4)

29.

(1)

(2)

(3)

(4)

30. M R

(1) Mmg

M m( ) (2) Mmg

M m( ) 2

(3) Mmg

m m( ) 3(4)

Mmg

M m( ) 4

31. y-

x- 2

(1) 46 kg-m2 (2) 92kg-m2

(3) 184 kg-m2 (4) 276 kg-m2


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32. A particle is oscillating in SHM. What fraction of total energy

is kinetic when the particle is at A/2 (A = Amplitude) from

the mean position

(1) 3

4

(2) 2

4

(3) 4

7

(4) 5

7

33. The time period of a simple pendulum of length L as

measured in an elevator descending with accelerationg

3

is -

(1) 23L

g

(2) 3L

g

F

HG

I

KJ

(3) 23

2

L

g

F

HG

I

KJ

(4) 22

3

L

g

34. The angular frequency of motion whose equation is

42

2

d y

dt + 9y = 0 is (y = displacement and t = time)

(1) 9

4(2)

4

9

(3) 3

2(4)

2

3

35. A simple pendulum is taken from the equator to the pole.

Its period -

(1) Decrease

(2) Increase

(3) Remains the same

(4) Decrease and then increases

32.

A/2 (A = )

(1) 3

4

(2) 2

4

(3) 4

7

(4) 5

7

33.g

3 L

(1) 23L

g

(2) 3L

g

F

HG

I

KJ

(3) 23

2

L

g

F

HG

I

KJ

(4) 22

3

L

g

34. 42

2

d y

dt + 9y = 0

(y = t = )

(1) 9

4(2)

4

9

(3) 3

2(4)

2

3

35.

(1)

(2)

(3)

(4)


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36. The dimensions of moment of intertia is -

(1) [M1L2T–1]

(2) [M0L–2T0]

(3) [M0L2T2]

(4) [M1L2T0]

37. If a spring has time period T, and is cut into n equal parts,

then the time period of each part will be -

(1) T n

(2) T

n

(3) nT

(4) T

38. Four massless springs whose force constants are 2k, 2k, k

and 2k respectively are attached to a mass M kept on a

frictionless plane (as shown in figure). If the mass M is

displaced in the horizontal direction, then the frequency of

the system -

2k 2k

2k

k

M

(1) 1

2 4k

M

(2) 1

2

4

k

M

(3) 1

2 7k

M

(4) 1

2

7

k

M

39. The amplitude of a particle executing simple harmonic

motion is a. At what displacement the kinetic energy will

be equal to the potential energy -

(1) zero (2) a/2

(3) a/ 2 (4) 3a/4

36.

(1) [M1L2T–1]

(2) [M0L–2T0]

(3) [M0L2T2]

(4) [M1L2T0]

37. T n

(1) T n

(2) T

n

(3) nT

(4) T

38. 2k, 2k, k 2k

M M

2k 2k

2k

k

M

(1) 1

2 4k

M

(2) 1

2

4

k

M

(3) 1

2 7k

M

(4) 1

2

7

k

M

39. a

(1) (2) a/2

(3) a/ 2 (4) 3a/4


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40. A thin wire of length L and uniform linear mass density is

bent into a circular loop with centre at O as shown in figure.

The moment of inertia of the loop about the axis XX' is-

(1)

L3

28(2)

L3

216(3)

5

16

3

2

L (4)

3

8

3

2

L

41. A particle is moving in a circle with uniform speed. Its motion is

(1) aperiodic

(2) periodic and simple harmonic

(3) periodic but not simple harmonic

(4) none of the above

42. Given

F i j 4 10 e j and

r i j 5 3

e j , compute torque.

(1) 62j unit (2) 62 k unit

(3) 48 i unit (4) 48 k unit

43. The initial angular velocity of fly wheel of moment of inertia

2Kg-m2, is 50 radian/sec. A torque of 10 N-m acts on it.

The time in which it gets accelerated to 80 radians/sec will

be -

(1) 12 sec (2) 2 sec

(3) 6 sec (4) 8 sec

44. If Kr and K

t refers to rotational and translational K.E. of an

object in pure rolling motion respectively then true

statement are -

(1) For disc Kr = 50% of K

t

(2) For shell Kr = 33% of K

t

(3) For solid sphere Kr = 50% of K

t

(4) None of these

45. Out of the two eggs, both equal in weight and indentical in

shape and size, one is raw and the other is half boiled. The

ratio between the moment of inertia of raw to boiled one,

about a central axis, will be -

(1) one (2) greather than one

(3) less than one (4) none of these

40. L

O

XX'

(1)

L3

28(2)

L3

216(3)

5

16

3

2

L(4)

3

8

3

2

L

41.

(1)

(2)

(3)

(4)

42. r i j 5 3

e j r i j 5 3

e j ,

(1) 62j (2) 62 k

(3) 48 i (4) 48 k

43. 2Kg-m2 50

radian/sec 10 N-m

80 radians/sec

(1) 12 sec (2) 2 sec

(3) 6 sec (4) 8 sec

44. Kr

Kt

(1) Kr = K

t 50%

(2) Kr = K

t 33%

(3) Kr = K

t 50%

(4)

45.

(1) (2)

(3) (4)


p-3 : com, rotational dynamics & shmapi.coachingapis.coachinglog.in/storage/162583/vs... · 2...

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