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This mock test of Test: Centre of Mass- 2 for Class 11 helps you for every Class 11 entrance exam.
This contains 25 Multiple Choice Questions for Class 11 Test: Centre of Mass- 2 (mcq) to study with solutions a complete question bank.
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*Multiple options can be correct

QUESTION: 1

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

Solution:

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

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.

Solution:

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

*Multiple options can be correct

QUESTION: 3

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

Solution:

- It can’t be since the integral would yield a value much greater than R/2
- It can’t be since the integral would yield a value much less than R/2
- Assuming the rate of increase and decrease is same the COM could lie in the centre
- Assuming the rate of increase and decrease is same the COM could lie in the centre

*Multiple options can be correct

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?

Solution:

*Multiple options can be correct

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

Solution:

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 x^{2}_{max} = ½ μ V^{2}_{rel}

So, x_{max} = 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

*Multiple options can be correct

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,

Solution:

*Multiple options can be correct

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.

Solution:

*Multiple options can be correct

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.

Solution:

*Multiple options can be correct

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 :

Solution:

*Multiple options can be correct

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.

Solution:

- The velocities of both the masses are always positive hence same direction
- The KE will be min when Vr = Vs which is at 2ms
- The dp
_{r}/dt = dp_{s}/dt and as we can see in the graph dv_{r}/dt < dv_{s}/dt, so mass of R is greater

*Multiple options can be correct

QUESTION: 11

In an inelastic collision,

Solution:

*Multiple options can be correct

QUESTION: 12

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

Solution:

*Multiple options can be correct

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

Solution:

QUESTION: 14

An isolated rail car original moving with speed v_{0} 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

Solution:

*Multiple options can be correct

QUESTION: 15

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

Solution:

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.

*Multiple options can be correct

QUESTION: 16

A particle of mass m moving horizontal with v_{0} 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 v_{2} is

Solution:

*Multiple options can be correct

QUESTION: 17

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

Solution:

*Multiple options can be correct

QUESTION: 18

The maximum height h attained by the particle is

Solution:

*Multiple options can be correct

QUESTION: 19

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

Solution:

*Multiple options can be correct

QUESTION: 20

Suppose the particle when reaches the horizontal surfaces, its velocity with respect to ground is v_{1} and that of wedge is v_{2}. Choose the correct statement (s)

Solution:

*Multiple options can be correct

QUESTION: 21

Choose the correct statement(s) related to particle m

Solution:

*Multiple options can be correct

QUESTION: 22

Choose the correct statement related to the wedge M

Solution:

*Multiple options can be correct

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

Solution:

*Multiple options can be correct

QUESTION: 24

Tension in string when it is vertical, is

Solution:

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.

*Multiple options can be correct

QUESTION: 25

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

Solution:

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