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Test: Centre of Mass - 2


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Test: Centre of Mass - 2 - Question 1

A body has its centre of mass at the origin. The x-coordinates of the particles

Detailed Solution for Test: Centre of Mass - 2 - Question 1

The y coordinates of the particles of the body may be all non zero and positive for some cases and negative in other cases.

Test: Centre of Mass - 2 - Question 2

An object comprises of a uniform ring of radius R and its uniform chord AB (not necessarily made of the same material) as shown. Which of the following can not be the centre of mass of the object.

                                

Detailed Solution for Test: Centre of Mass - 2 - Question 2




Since the points must have symmetric coordinates so B is the answer.

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Test: Centre of Mass - 2 - Question 3

In which of the following cases the centre of mass of a an rod is certainly not at its centre ?

Detailed Solution for Test: Centre of Mass - 2 - Question 3
  1. It can’t be since the integral would yield a value much greater than R/2
  2. It can’t be since the integral would yield a value much less than R/2
  3. Assuming the rate of increase and decrease is same the COM could lie in the centre
  4. Assuming the rate of increase and decrease is same the COM could lie in the centre
     
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Test: Centre of Mass - 2 - Question 4

Consider following statements

[1] CM of a uniform semicircular disc of radius R = 2R/p from the centre

[2] CM of a uniform semicircular ring of radius R = 4R/3p from the centre

[3] CM of a solid hemisphere of radius R = 4R/3p from the centre

[4] CM of a hemisphere shell of radius R = R/2 from the centre

Which statements are correct?

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Test: Centre of Mass - 2 - Question 5

Two blocks A (5kg) and B(2kg) attached to the ends of a spring constant 1120 N/m are placed on a smooth horizontal plane with the spring undeformed. Simultaneously velocities of 3m/s and 10m/s along the line of the spring in the same direction are imparted to A and B then

                                  

Detailed Solution for Test: Centre of Mass - 2 - Question 5

Vcm = m1v1 + m2v2/m1 + m2 = 5m/s
So, Vrela = -2m/s and Vrelb = 5m/s
Now, Va = 5m/s and Vb = 5m/s
Also, ½ K x2max = ½ μ V2rel 
So, xmax = ¼ m = 25 cm
Now, since the time periods of both the blocks are same so they will be at max compression and elongation alternatively
 

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Test: Centre of Mass - 2 - Question 6

Two identical balls are interconnected with a massless and inextensible thread. The system is in gravity free space with the thread just taut. Each ball is imparted a velocity v, one towards the other ball and the other perpendicular to the first, at t = 0. Then,

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Test: Centre of Mass - 2 - Question 7

A ball moving with a velocity v hits a massive wall moving towards the ball with a velocity u. An elastic impact lasts for a time Dt.

Detailed Solution for Test: Centre of Mass - 2 - Question 7

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Test: Centre of Mass - 2 - Question 8

A particle moving with kinetic energy = 3 joule makes an elastic head on collision with a stationary particle when has twice its mass during the impact.

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Test: Centre of Mass - 2 - Question 9

Two balls A and B having masses 1 kg and 2 kg, moving with speeds 21 m/s and 4 m/s respectively in opposite direction, collide head on. After collision A moves with a speed of 1 m/s in the same direction, then correct statements is :

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Test: Centre of Mass - 2 - Question 10

The diagram to the right shown the velocity-time graph for two masses R and S that collided elastically. Which of the following statements is true?

                     

(I) R and S moved in the same direction after the collision.

(II) Kinetic energy of the system (R & S) is minimum at t = 2 milli sec.

(III) The mass of R was greater than mass of S.

Detailed Solution for Test: Centre of Mass - 2 - Question 10
  1. The velocities of both the masses are always positive hence same direction
  2. The KE will be min when Vr = Vs which is at 2ms
  3. The dpr/dt = dps/dt and as we can see in the graph dvr/dt < dvs/dt, so mass of R is greater
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Test: Centre of Mass - 2 - Question 11

In an inelastic collision,

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Test: Centre of Mass - 2 - Question 12

In a one-dimensional collision between two particles, their relative velocity is before the collision and  after the collision

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Test: Centre of Mass - 2 - Question 13

A set of n-identical cubical blocks lie at rest parallel to each other along a line on a smooth horizontal surface. The separation between the near surfaces of any two adjacent blocks is L. The block at one end is given a speed V towards the next one at time t = 0. All collision are completely inelastic, then

Test: Centre of Mass - 2 - Question 14

An isolated rail car original moving with speed v0 on a straight, frictionless, level track contains a large amount of sand. A release value on the bottom of the car malfunctions, and sand begins to pour out straight down relative to the rail car.

(a) Is momentum conserved in this process?

(A) The momentum of the rail car along is conserved

(B) The momentum of the rail car + sand remaining within the car is conserved

(C) The momentum of the rail car + all of the sand, both inside and outside the rail car, is conserved

(D) None of the three previous systems have momentum conservation

(b) What happens to the speed of the rail car as the sand pours out?

(A) The car begins to roll faster

(B) The car maintains the same speed

(C) The car begins to slow down

(D) The problem cannot be solved since momentum is not conserved


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Test: Centre of Mass - 2 - Question 15

 If the external forces acting on a system have zero resultant, the centre of mass

Detailed Solution for Test: Centre of Mass - 2 - Question 15

If the external force acting on a system have zero resultant forces, then the total momentum remains constant i.e. conserved. Hence, the center of mass remains at rest or moves with a constant velocity.

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Test: Centre of Mass - 2 - Question 16

A particle of mass m moving horizontal with v0 strikes a smooth wedge of mass M, as shown in figure. After collision, the ball starts moving up the inclined face of the wedge and rises to a height h.

The final velocity of the wedge v2 is

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Test: Centre of Mass - 2 - Question 17

When the particle has risen to a height h on the wedge, then choose the correct alternative(s)

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Test: Centre of Mass - 2 - Question 18

The maximum height h attained by the particle is

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Test: Centre of Mass - 2 - Question 19

Identify the correct statement(s) related to the situation when the particle starts moving downward.

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Test: Centre of Mass - 2 - Question 20

Suppose the particle when reaches the horizontal surfaces, its velocity with respect to ground is v1 and that of wedge is v2. Choose the correct statement (s)

                      

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Test: Centre of Mass - 2 - Question 21

Choose the correct statement(s) related to particle m

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Test: Centre of Mass - 2 - Question 22

Choose the correct statement related to the wedge M

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Test: Centre of Mass - 2 - Question 23

A small ball B of mass m is suspended with light inelastic string of length L from a block A of same mass m which can move on smooth horizontal surface as shown in the figure. The ball is displaced by angle q from equilibrium position & then released.

                                

The displacement of block when ball reaches the equilibrium position is

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Test: Centre of Mass - 2 - Question 24

Tension in string when it is vertical, is

Detailed Solution for Test: Centre of Mass - 2 - Question 24

Tension in string when it is vertical, is Mg. Since nothing else has been provided so we assume all the forces are in the desired directions.

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Test: Centre of Mass - 2 - Question 25

Maximum velocity of block during subsequent motion of the system after release of ball is

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