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Centre of Mass, Linear Momentum, Collision Physics - Centre of Mass, Linear Momentum, Collision

Gujarat Board (GSEB) - STD 12 Science - Physics (GSEB - English Medium). 110 questions in this chapter.

Question types

Centre of Mass, Linear Momentum, Collision question types

110 questions across 6 question groups — pick any mix to generate a Physics paper with step-by-step answer keys.

110
Questions
6
Question groups
5
Question types
Sample Questions

Centre of Mass, Linear Momentum, Collision questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
A uniform sphere is placed on a smooth horizontal surface and a horizontal force F is applied on it at a distance h above the surface. The acceleration of the centre:
  • A
    Is maximum when h = 0.
  • B
    Is maximum when h = R.
  • ✓
    Is maximum when h = 2R.
  • D
    Is independent of h.

Answer: C.

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Q 2M.C.Q (1 Marks)1 Mark
Two balls are thrown simultaneously in air. The acceleration of the centre of mass of the two balls while in air:
  • A
    Depends on the direction of the motion of the balls.
  • B
    Depends on the masses of the two balls.
  • C
    Depends on the speeds of the two balls.
  • ✓
    Is equal to g.

Answer: D.

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Q 3M.C.Q (1 Marks)1 Mark
Consider the following two statements:
  1. The linear momentum of a particle is independent of the frame of reference.
  2. The kinetic energy of a particle is independent of the frame of reference.
  • A
    Both $A$ and $B$ are true.
  • B
    $A$ is true but $B$ is false.
  • C
    $A$ is false but $B$ is true.
  • ✓
    Both $A$ and $B$ are false.

Answer: D.

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Q 4M.C.Q (1 Marks)1 Mark
A ball kept in a closed box moves in the box making collisions with the walls. The box is kept on a smooth surface. The velocity of the centre of mass:
  • A
    Of the box remains constant.
  • ✓
    Of the box plus the ball system remains constant.
  • C
    Of the ball remains constant.
  • D
    Of the ball relative to the box remains constant.

Answer: B.

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Q 5M.C.Q (1 Marks)1 Mark
In an inelastic collision:
  • A
    The initial kinetic energy is equal to the final kinetic energy.
  • ✓
    The final kinetic energy is less than the initial kinetic energy.
  • C
    The kinetic energy remains constant.
  • D
    The kinetic energy first increases then decreases.

Answer: B.

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Q 61 Marks Question1 Mark
Suppose we define a quantity 'Linear Pomentum' as linear pomentum = mass × speed. The linear pomentum of a system of particles is the sum of linear pomenta of the individual particles. Can we state a principle of conservation of linear pomentum as ''linear pomentum of a system remains constant if no external force acts on it?''
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Q 71 Marks Question1 Mark
A ball is moved on a horizontal table with some velocity. The ball stops after moving some distance. Which external force is responsible for the change in the momentum of the ball?
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Q 91 Marks Question1 Mark
Use the definition of linear pomentum from the previous question. Can we state the principle of conservation of linear pomentum for a single particle?
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Q 112 Marks Questions2 Marks
To accelerate a car we ignite petrol in the engine of the car. Since only an external force can accelerate the centre of mass, is it proper to say that ''the force generated by the engine accelerates the car?''
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Q 122 Marks Questions2 Marks
A uranium-238 nucleus, initially at rest, emits an alpha particle with a speed of $1.4 x 10^7 \ m/s$. Calculate the recoil speed of the residual nucleus thorium-234. Assume that the mass of a nucleus is proportional to the mass number.
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Q 132 Marks Questions2 Marks
A bob suspended from the ceiling of a car which is accelerating on a horizontal road. The bob stays at rest with respect to the car with the string making an angle $\theta$ with the vertical. The linear momentum of the bob as seen from the road is increasing with time. Is it a violation of conservation of linear momentum? If not, where is the external force which changes the linear momentum?
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Q 142 Marks Questions2 Marks
Consider a gravity-free hall in which a tray of mass M, carrying a cubical block of ice of mass m and edge L, is at rest in the middle. If the ice melts, by what distance does the centre of mass of "the tray plus the ice" system descend?
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Q 163 Marks Question3 Marks
Two blocks of masses $m_1$ and $m_2$ are connected by a spring of spring constant k. The block of mass $m_2$ is given a sharp impulse so that it acquires a velocity $v_0$ towards right. Find
  1. The velocity of the centre of mass.
  2. The maximum elongation that the spring will suffer.
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Q 173 Marks Question3 Marks
Light in certain cases may be considered as a stream of particles called photons. Each photon has a linear momentum $\frac{\text{h}}{\lambda}$ where h is the Planck's constant and $\lambda$ is the wavelength of the light. A beam of light of wavelength $\lambda$ is incident on a plane mirror at an angle of incidence $\theta.$ Calculate the change in the linear momentum of a photon as the beam is reflected by the mirror.
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Q 183 Marks Question3 Marks
The centre of mass is defined as $\overrightarrow{\text{R}}=\frac{1}{\text{M}}\sum\limits_\text{i}\text{m}_\text{i}\overrightarrow{\text{r}_{\text{i}}}.$ Suppose we define "centre of charge" as $\overrightarrow{\text{R}}_\text{c}=\frac{1}{\text{Q}}\sum\limits_\text{i}\text{q}_\text{i}\overrightarrow{\text{r}_{\text{i}}}$ where $q_i$ represents the $i^{th}$ charge placed at $\overrightarrow{\text{r}_\text{i}}$ and Q is the total charge of the system.
  1. Can the centre of charge of a two-charge system be outside the line segment joining the charges?
  2. If all the charges of a system are in X-Y plane, is it necessary that the centre of charge be in X-Y plane?
  3. If all the charges of a system lie in a cube, is it necessary that the centre of charge be in the cube?
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Q 203 Marks Question3 Marks
The balloon, the light rope and the monkey shown in figure are at rest in the air. If the monkey reaches the top of the rope, by what distance does the balloon descend ? Mass of the balloon = M, mass of the monkey = m and the length of the rope ascended by the monkey = L.
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Q 215 Marks Questions5 Marks
A square plate of edge d and a circular disc of diameter d are placed touching each other at the midpoint of an edge of the plate as shown in figure. Locate the centre of mass of the combination, assuming same mass per unit area for the two plates.
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Q 225 Marks Questions5 Marks
The structure of a water molecule is shown in figure. Find the distance of the centre of mass of the molecule from the centre of the oxygen atom.
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Q 235 Marks Questions5 Marks
A bullet of mass 20g travelling horizontally with a speed of 500m/s passes through a wooden block of mass 10.0kg initially at rest on a level surface. The bullet emerges with a speed of 100m/s and the block slides 20cm on the surface before coming to rest. Find the friction coefficient between the block and the surface.
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Q 245 Marks Questions5 Marks
A uniform disc of radius R is put over another uniform disc of radius 2R of the same thickness and density. The peripheries of the two discs touch each other. Locate the centre of mass of the system.
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Q 255 Marks Questions5 Marks
A block of mass 200g is suspended through a vertical spring. The spring is stretched by 1.0cm when the block is in equilibrium. A particle of mass 120g is dropped on the block from a height of 45cm. The particle sticks to the block after the impact. Find the maximum extension of the spring. Take $g = 10m/s^2.$​​​​​​​
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Q 26Case study (4 Marks)4 Marks
What can be said about the centre of mass of a uniform hemisphere without making any calculation? Will its distance from the centre be more than $\frac{\text{r}}{2}$ or less than $\frac{\text{r}}{2}?$
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Q 27Case study (4 Marks)4 Marks
A fat person is standing on a light plank floating on a calm lake. The person walks from one end to the other on the plank. His friend sitting on the shore watches him and finds that the person hardly moves any distance because the plank moves backward about the same distance as the person moves on the plank. Explain.
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Q 28Case study (4 Marks)4 Marks
Two fat astronauts each of mass 120kg are travelling in a closed spaceship moving at a speed of 15km/s in the outer space far removed from all other material objects. The total mass of the spaceship and its contents including the astronauts is 660kg. If the astronauts do slimming exercise and thereby reduce their masses to 90kg each, with what velocity will the spaceship move?
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Q 29Case study (4 Marks)4 Marks
You are holding a cage containing a bird. Do you have to make less effort if the bird flies from its position in the cage and manages to stay in the middle without touching the walls of the cage? Does it make a difference whether the cage is completely closed or it has rods to let air pass?
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Q 30Case study (4 Marks)4 Marks
A collision experiment is done on a horizontal table kept in an elevator. Do you expect a change in the results if the elevator is accelerated up or down because of the noninertial character of the frame?
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