- Introduction
- |
- Center of Mass
- |
- Position of center of mass
- |
- Position vector of centre of mass in terms of co-ordinate components
- |
- Motion of centre of mass
- |
- Acceleration of centre of mass
- |
- Kinetic energy of the system of particles
- |
- Two particle system and reduced mass
- |
- Collisions
- |
- Head on elastic collision of two particles
- |
- Head on inelastic collision of two particles
- |
- Deflection of an moving particle in two dimension
- Solved examples

- Included with Linear momentum
- Assignment 1
- |
- Assignment 2
- |
- Assignment 3
- |
- Assignment 4

- Included with Linear momentum
- How to solve center of mass problems

t

a. t

b. t

c t

d Depends on the mass of the body

a. v

b. v

c. v

d. v

a. 2 kg, (6 m/s)i

b. 2 kg, (-6 m/s)i

c. 2 kg, (3 m/s)i

d. 2 kg, (-3 m/s)i

a. Momentum Alone

b KE alone

c. Both Momentum and KE

d. Neither KE nor momentum

a.(-2i-3j)10

b. (2i+3j)10

c (2i-3j)10

d. none of these

a.m

b.mu

c. (m+M)u

d. mMu

a.p

b. p/2Mgs

c. p

d. p/2M

a. Workdone between two points is independent of the path

b. Workdone in a closed loop is zero

c. if the workdone by the conservative is positive,its potential energy increases

d. None of the these

a.The freqiency is independent of the acceleration due to gravity g

b.The period depends on the amplitude of the ocsillation

c.the period is independent of mass m

d. the period is independent of lenght l

a.v

b.v

c. v

d. v

a.&radic:2gl

b. &radic:2gl(1-cosθ)

c.&radic:2glcosθ

d.&radic:2gl(1-sinθ

a. Linear momentum

b.mass

c.energy

d. angular momentum

a.wu/w+W

b. Wu/W+w

c. (W+w)u/w

d. none of the above

a 40 J

b. 42.2 J

c. 42.6 J

d. 45 J

STATEMENT 1 Linear momentum of a system of particles is zero.

STATEMENT 2 Kinetic energy of system of particles is zero.

(A) A does not imply B and B does not imply A.

(B) A implies B but B does not imply A

(C) A does not imply B but b implies A’

(D) A implies B and B implies A.

a.r=(2R/π)j

b.r=(R/π)j

c.r=(4R/π)j

d. none of the these

a.if Workdone by the conservative force is positive then Potential energy decreases

b. Rate of change of momentum of many particles system is proportional to net external force on the system

c.The workdone by the conservative force in closed loop is zero

d. None of the above

a. e

b. zero

c. e

d. none of the above

U=20x

a. -40xi-105z

b. 40xi-105z

c.-10xi-105z

d 40xi+105z

Matrix Match type

Column I

a. Frictional force

b. Gravitational force

c. Electrical force

d Viscous force

Column II

P. Workdone by the force in closed loop is zero

Q. Workdone by the force in closed loop is not zero

a. L

b. L/4

c. L/2

d. 2L

a. is zero

b. remains constant

c. goes on increasing

d. goes on decreasing

a. Up the incline while ascending and down the incline while descending

b.Up the incline while ascending and desending

c. down the incline while ascending and up the incline while descending

d.down the incline while ascending and desending

a. 28.6 m

b 30 m

c. 28 m

d. none of these

a. (2/3)gsinθ

b.(2/3)gcosθ

c gsinθ

d none of these

a. 5.26 rev/s

b. 5.2 rev/s

c 4.7 rev/s

d. none of thes

a. 7ML

b.7ML

c. 11ML

d.ML

acceleration vector for a point on the rim:

a. increases in magnitude but retains the same angle with the tangent to the rim

b.increases in magnitude and becomes more nearly radial

c. increases in magnitude and becomes more nearly tangent to the rim

d. decreases in magnitude and becomes more nearly radial

Two wheels are identical but wheel B is spinning with twice the angular speed of wheel A. The ratio of the

magnitude of the &radical acceleration of a point on the rim of B to the magnitude of the radial acceleration of

a point on the rim of A is:

a. 4

b . 2

c 1/2

d 1/4

the speed of a point on the rim to the speed of a point halfway between the center and the rim is:

a 2

b 1/2

c 4

d 1/4

slowing at first. What time elapses before its angular velocity is18 rad/s in the direction opposite to its initial

angular velocity?

a 3 sec

b 6 sec

c 18 sec

d none of these

(A) I

(B) I

(C) I

(D) I

Where D

a. A train which speeding Up

b. A train with constant speed

c. A train which speeding down

d A train at rest

a. Velcoity is perpendicular to acceleration at the highest point

b. Horizontal components of velocity remains constant through out the path

c. Range of the projectile is given by Horizontal component of velocity X Time of flight

d. None of the above

a)Pm/m+M

b)P

c)PM/m+M

d)Pm/M-m

(A) 24 N

(B) 74 N

(C) 15 N

(D) 49 N

x=t

Find the acceleration of the particle at displacement equal to zero

a.(-8,-2,10)

b. (-1,-2,10)

c. (8,2,10)

d. (1,2,10)

a. 2 kg, (6 m/s)i

b. 2 kg, (-6 m/s)i

c. 2 kg, (3 m/s)i

d. 2 kg, (-3 m/s)i

Total momentum=(18 kgm/sec)i

velocity of Center of mass=(3 m/s)i.

Mass of one object=4 kg

Velocity of this object=(1.5 m/s)i

let m be the mass of other object

And v be the velocity

Now we know total momentum =Total massX velocity of center of mass

(18 kgm/sec)i=(m+4)(3 m/s)i.

or m=2 kg

Now V

or

3i=(4*1.5i + 2v)/6

or 18i=6i+2v

v=6i m/sec

hence a is correct

a.r=(2R/π)j

b.r=(R/π)j

c.r=(4R/π)j

d. none of the these

Consider a differential element of lenght dl of the ring whose radius vector makes an angle θ with the x-axis .If the angle subtended by the length dl is dθ at the center then,dl=Rdθ

Let λ be the mass per unit length

Then mass of this element is dm=λRdθ

X

Y

or Y

Hence A is correct.

a. e

b. zero

c. e

d. none of the above

Since there are no external force on the system,center of mass remains at rest so acceleration is zero

b.100m

c.80m

d.90

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