33 Years NEET-AIPMT Chapterwise Solutions - Physics 2020
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33 Years NEET-AIPMT Chapterwise Solutions - Physics 2020

All previous year questions , and these are downloaded from the sources in the internet. I don't own these resources and these are copyrighted by MTG. All previous year questions , and these are downloaded from the sources in the internet. I don't own these resources and these are copyrighted by MTG.

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Telegram @unacademyplusdiscounts50 NEET-AIPMT Chapterwise Topicwise Solutions PhysicsCHAPTER7Systems ofParticles andRotational Motion7.2 Centre of Mass1. Two particles of mass 5 kg and 10 kg respectively areattached to the two ends of a rigid rod of length 1 mwith negligible mass. The centre of mass of the systemfrom the 5 kg particle is nearly at a distance of(a) 33 cm(b) 50 cm(c) 67 cm (d) 80 cm (NEET 2020)2. Three masses are placed on the x-axis : 300 g atorigin, 500 g at x = 40 cm and 400 g at x = 70 cm.The distance of the centre of mass from the origin is(a) 40 cm(b) 45 cm(c) 50 cm (d) 30 cm (Mains 2012)3. Two bodies of mass 1 kg and 3 kg have position vectors^ i ^ ^ ^ j k i j ^ ^,+ 2 + and −3 − 2+ k respectively. The centreof mass of this system has a position vector^ ^ ^(a) −2 i − j+k (b) 2 ^ i − j ^ −2k^^ ^ ^(c) − i + j+k(d) − 2 ^ i + 2k^ (2009)4. Consider a system of two particles having masses m 1and m 2 . If the particle of mass m 1 is pushed towardsthe centre of mass of the particles through a distanced, by what distance would be particle of mass m 2move so as to keep the centre of mass of the particlesat the original position ?(a)m1m m d1+2(b) m 1m d2(c) d(d) m 2m d(2004)15. Three identical metal balls, each of radius r areplaced touching each other on a horizontal surfacesuch that an equilateral triangle is formed whencentres of three balls are joined. The centre of themass of the system is located at(a) line joining centres of any two balls(b) centre of one of the balls(c) horizontal surface(d) point of intersection of the medians. (1999)6. The centre of mass of system of particles does notdepend on(a) position of the particles(b) relative distances between the particles(c) masses of the particles(d) forces acting on the particle. (1997)7.3 Motion of Centre of Mass7. Two persons of masses 55 kg and 65 kg respectively,are at the opposite ends of a boat. The length of theboat is 3.0 m and weighs 100 kg. The 55 kg manwalks up to the 65 kg man and sits with him. If theboat is in still water the center of mass of the systemshifts by(a) 3.0 m (b) 2.3 m (c) zero (d) 0.75 m(2012)8. Two particles which are initially at rest, movetowards each other under the action of their internalattraction. If their speeds are v and 2v at any instant,then the speed of centre of mass of the system will be(a) 2v (b) zero (c) 1.5v (d) v (2010)9. A man of 50 kg mass is standing in a gravity freespace at a height of 10 m above the floor. He throws astone of 0.5 kg mass downwards with a speed 2 m/s.When the stone reaches the floor, the distance of theman above the floor will be(a) 9.9 m(b) 10.1 m(c) 10 m (d) 20 m (2010)7.5 Vector Product of Two Vectors 10. Vectors, A, B and C are such that A ⋅ B=0and AC ⋅ =0. Then the vector parallel to A is (a) A× B(b) B+C (c) B× C(d) B and C(Karnataka NEET 2013) 11. A and B are two vectors and q is the angle between them, if | A× B| = 3 ( A⋅B), the value of q is(a) 45° (b) 30° (c) 90° (d) 60° (2007)12. If the angle between the vectors A and B is q, thevalue of the product ( B× A)⋅ A is equal to(a) BA 2 sinq (b) BA 2 cosq(c) BA 2 sinqcosq (d) zero. (2005, 1989)

Telegram @unacademyplusdiscountsSystems of Particles and Rotational Motion 13. If | A× B|= 3 A⋅B then the value of | A+ B|is12 /(a) (A 2 + B 2 + AB) 1/2 ⎛ AB(b)2 2 ⎞A + B +⎝⎜3 ⎠⎟2 212(c) A + B (d) ( A + B + 3AB) / (2004)14. The resultant of A × 0 will be equal to(a) zero(b) A(c) zero vector (d) unit vector. (1992)7.6 Angular Velocity and its Relation withLinear Velocity15. What is the value of linear velocity, if ^ ^ ^ ^ ^ ^r = 3i − 4j + k and ω= 5i− 6j+6k?^ ^ ^(a) 4i− 13j+ 6k^ ^ ^(b) 18 i+ 13 j−2k^ ^ ^(c) 6i+ 2j− 3k^ ^ ^(d) 6i− 2j+ 8k(1999)7.7 Torque and Angular Momentum16. Find the torque about the origin when a force of 3 j^ Nacts on a particle whose position vector is 2k^ m .(a) 6 i^ N m (b) 6 j^ N m(c) −6 i^ N m (d) 6k^ N m (NEET 2020)17. The moment of the force, ^ ^ ^F = 4i+ 5j − 6kat(2, 0, –3), about the point (2, –2, –2), is given by^ ^ ^(a) −8i−4j − 7 k (b) −4i − j − 8k^ ^ ^(c) −7i−8j − 4 k^ ^ ^(d) −7i−4j − 8k(NEET 2018)18. A forceF = α^ i+ 3 ^ j+6 kis acting at a point ^ ^r = 2i−6j−12k. The value of a for which angularmomentum about origin is conserved is(a) zero (b) 1 (c) –1 (d) 2 (2015)19. A mass m moves in a circle on a smooth horizontalplane with velocity v 0 at a radius R 0 . The mass isattached to a string which passes through a smoothhole in the plane as shown. The tension in the stringis increased gradually and finally m moves in a circleof radius R 0. The final value of the kinetic energy is2(a) 2mv0 2 (b) 1 mv 0 222(c) mv 0 (d) 1 mv 0 2 (2015 Cancelled)420. When a mass is rotating in a plane about a fixedpoint, its angular momentum is directed along(a) a line perpendicular to the plane of rotation(b) the line making an angle of 45° to the plane ofrotation51(c) the radius(d) the tangent to the orbit. (2012)21. A small mass attached to a string rotates on africtionless table top as shown. If the tension in thestring is increased by pulling the string causing theradius of the circular motion to decrease by a factorof 2, the kinetic energy of the mass will(a) decrease by a factor of 2(b) remain constant(c) increase by a factor of 2(d) increase by a factor of 4 (Mains 2011)22. If F is the force acting on a particle having positionvector r and τ be the torque of this force about theorigin, then(a) r ⋅ τ> 0and F⋅ τ<0 (b) r ⋅ τ= 0andF⋅ τ=0 (c) r ⋅ τ= 0 and F⋅τ≠0(d) r ⋅τ≠0 and F⋅ τ=0 (2009)23. A particle of mass m moves in the XY plane with avelocity v along the straight line AB. If the angularmomentum of the particle with respect to origin Ois L A when it is at A and L B when it is at B, then(a) L A = L B(b) the relationship between L A and L B dependsupon the slope of the line AB(c) L A < L B (d) L A > L B (2007)24. Find the torque of a force F ^ ^ ^=− 3i+ j+5kacting atthe point r ^ ^= 7i + 3j+k^.^ ^ ^(a) − 21i + 4 j+4 k^ ^ ^(b) − 14 i + 34 j−16k^ ^ ^(c) 14 i − 38 j+ 16k^ ^ ^(d) 4i + 4 j+ 6k (1997)25. What is the torque of the force F ^ ^ ^= 2i − 3j+4 k Nacting at the point r ^ ^ ^= 3i + 2j+3km about origin?^ ^ ^^ ^ ^(a) − 6i + 6j−12k(b) − 17 i + 6j+13k^ ^ ^^ ^ ^(c) 6i − 6j+ 12k(d) 17 i −6j− 13k(1995)26. A particle of mass m = 5 is moving with a uniformspeed v = 3 2 in the XOY plane along the liney = x + 4. The magnitude of the angular momentumof the particle about the origin is(a) 60 units (b) 40 2units(c) zero (d) 7.5 units (1991)7.8 Equilibrium of a Rigid Body27. Which of the following statements are correct?(1) Centre of mass of a body always coincides withthe centre of gravity of the body.(2) Centre of mass of a body is the point at whichthe total gravitational torque on the body is zero.(3) A couple on a body produces both translationaland rotational motion in a body.(4) Mechanical advantage greater than one meansthat small effort can be used to lift a large load.

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50 NEET-AIPMT Chapterwise Topicwise Solutions Physics

CHAPTER

7

Systems of

Particles and

Rotational Motion

7.2 Centre of Mass

1. Two particles of mass 5 kg and 10 kg respectively are

attached to the two ends of a rigid rod of length 1 m

with negligible mass. The centre of mass of the system

from the 5 kg particle is nearly at a distance of

(a) 33 cm

(b) 50 cm

(c) 67 cm (d) 80 cm (NEET 2020)

2. 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

(a) 40 cm

(b) 45 cm

(c) 50 cm (d) 30 cm (Mains 2012)

3. Two bodies of mass 1 kg and 3 kg have position vectors

^ i ^ ^ ^ j k i j ^ ^,

+ 2 + and −3 − 2

+ k respectively. The centre

of mass of this system has a position vector

^ ^ ^

(a) −2 i − j+

k (b) 2 ^ i − j ^ −2k

^

^ ^ ^

(c) − i + j+

k

(d) − 2 ^ i + 2k

^ (2009)

4. Consider a system of two particles having masses m 1

and m 2 . If the particle of mass m 1 is pushed towards

the centre of mass of the particles through a distance

d, by what distance would be particle of mass m 2

move so as to keep the centre of mass of the particles

at the original position ?

(a)

m1

m m d

1+

2

(b) m 1

m d

2

(c) d

(d) m 2

m d

(2004)

1

5. Three identical metal balls, each of radius r are

placed touching each other on a horizontal surface

such that an equilateral triangle is formed when

centres of three balls are joined. The centre of the

mass of the system is located at

(a) line joining centres of any two balls

(b) centre of one of the balls

(c) horizontal surface

(d) point of intersection of the medians. (1999)

6. The centre of mass of system of particles does not

depend on

(a) position of the particles

(b) relative distances between the particles

(c) masses of the particles

(d) forces acting on the particle. (1997)

7.3 Motion of Centre of Mass

7. Two persons of masses 55 kg and 65 kg respectively,

are at the opposite ends of a boat. The length of the

boat is 3.0 m and weighs 100 kg. The 55 kg man

walks up to the 65 kg man and sits with him. If the

boat is in still water the center of mass of the system

shifts by

(a) 3.0 m (b) 2.3 m (c) zero (d) 0.75 m(2012)

8. Two particles which are initially at rest, move

towards each other under the action of their internal

attraction. If their speeds are v and 2v at any instant,

then the speed of centre of mass of the system will be

(a) 2v (b) zero (c) 1.5v (d) v (2010)

9. A man of 50 kg mass is standing in a gravity free

space at a height of 10 m above the floor. He throws a

stone of 0.5 kg mass downwards with a speed 2 m/s.

When the stone reaches the floor, the distance of the

man above the floor will be

(a) 9.9 m

(b) 10.1 m

(c) 10 m (d) 20 m (2010)

7.5 Vector Product of Two Vectors

10. Vectors, A, B and C are such that A ⋅ B

=0and

AC ⋅ =0. Then the vector parallel to A is

(a) A× B

(b) B+

C

(c) B× C

(d) B and C

(Karnataka NEET 2013)

11. A and B are two vectors and q is the angle between

them, if | A× B| = 3 ( A⋅

B)

, the value of q is

(a) 45° (b) 30° (c) 90° (d) 60° (2007)

12. If the angle between the vectors A

and B

is q, the

value of the product ( B× A)

⋅ A is equal to

(a) BA 2 sinq (b) BA 2 cosq

(c) BA 2 sinqcosq (d) zero. (2005, 1989)

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