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However, it may move uniformly with constant velocity. - Physics

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प्रश्न

If the external force acting on a system have zero resultant, the centre of mass
(a) must not move
(b) must not accelerate
(c) may move
(d) may accelerate.

टीपा लिहा

उत्तर

(b) must not accelerate
(c) may move

If the external force acting on a system has zero resultant,
then, acceleration of centre of mass \[= \frac{\vec{F}_{net}}{M} = 0\]
However, it may move uniformly with constant velocity.

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 9: Centre of Mass, Linear Momentum, Collision - MCQ [पृष्ठ १५९]

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एचसी वर्मा Concepts of Physics Vol. 1 [English] Class 11 and 12
पाठ 9 Centre of Mass, Linear Momentum, Collision
MCQ | Q 4 | पृष्ठ १५९

संबंधित प्रश्‍न

Give the location of the centre of mass of a

  1. sphere,
  2. cylinder,
  3. ring, and
  4. cube,

each of uniform mass density. Does the centre of mass of a body necessarily lie inside the body?


If all the particle of a system lie in a cube, is it necessary that the centre of mass be in the cube?


In a head-on collision between two particles, is it necessary that the particles will acquire a common velocity at least for one instant?


Consider the following the equations
(A) \[\vec{R} = \frac{1}{M} \sum_i m_i \vec{r_i}\] and
(B) \[\vec{a}_{CM} = \frac{\vec{F}}{M}\] 
In a noninertial frame


Consider a system of two identical particles. One of the particles is at rest and the other has an acceleration a. The centre of mass has an Acceleration


A nonzero external force acts on a system of particles. The velocity and the acceleration of the centre of mass are found to be v0 and a0 at instant t. It is possible that
(a) v0 = 0, a0 = 0
(b) v0 = 0, a0 ≠ 0
(c) v0 ≠ 0, a0 = 0
(d) v0 ≠ 0, a0 ≠ 0


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. 


Two fat astronauts each of mass 120 kg are travelling in a closed  spaceship moving at a speed of 15 km/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 660 kg. If the astronauts do slimming exercise and thereby reduce their masses to 90 kg each, with what velocity will the spaceship move?


A particle of mass 100 g moving at an initial speed u collides with another particle of same mass kept initially at rest. If the total kinetic energy becomes 0.2 J after the collision, what could be the minimum and the maximum value of u. 


A projectile is fired with a speed u at an angle θ above a horizontal field. The coefficient of restitution of collision between the projectile and the field is e. How far from the starting point, does the projectile makes its second collision with the field? 


The axis of rotation of a purely rotating body

(a) must pass through the centre of mass

(b) may pass through the centre of mass

(c) must pass through a particle of the body

(d) may pass through a particle of the body.


Consider a gravity-free hall in which an experimenter of mass 50 kg is resting on a 5 kg pillow, 8 ft above the floor of the hall. He pushes the pillow down so that it starts falling at a speed of 8 ft/s. The pillow makes a perfectly elastic collision with the floor, rebounds and reaches the experimenter's head. Find the time elapsed in the process. 


Two small balls A and B, each of mass m, are joined rigidly to the ends of a light rod of length L (see the following figure). The system translates on a frictionless horizontal surface with a velocity \[\nu_0\] in a direction perpendicular to the rod. A particle P of mass m kept at rest on the surface sticks to the ball A as the ball collides with it. Find
(a) the linear speeds of the balls A and B after the collision, (b) the velocity of the centre of mass C of the system A + B + P and (c) the angular speed of the system about C after the collision.

[Hint : The light rod will exert a force on the ball B
only along its length.]


Solve the following problem.

Four uniform solid cubes of edges 10 cm, 20 cm, 30 cm and 40 cm are kept on the ground, touching each other in order. Locate centre of mass of their system.


The centre of mass of a system of two particles divides the distance between them ______.


Which of the following has maximum momentum?


Centre of mass is a point ______.


The density of a non-uniform rod of length 1 m is given by ρ(x) = a(1 + bx2) where a and b are constants and 0 ≤ x ≤ 1. The centre of mass of the rod will be at ______.


Figure shows a lamina in x-y plane. Two axes z and z ′ pass perpendicular to its plane. A force F acts in the plane of lamina at point P as shown. Which of the following are true? (The point P is closer to z′-axis than the z-axis.)

  1. Torque τ caused by F about z axis is along `-hatk`.
  2. Torque τ′ caused by F about z′ axis is along `-hatk`.
  3. Torque τ caused by F about z axis is greater in magnitude than that about z axis.
  4. Total torque is given be τ = τ + τ′.

The spheres of masses 2 kg and 4 kg are situated at the opposite ends of wooden bars of length 9 m. Where does the centre of mass of the system will ______.


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