Advertisements
Advertisements
प्रश्न
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
उत्तर
(b) v0 = 0, a0 ≠ 0
(d) v0 ≠ 0, a0 ≠ 0
If a non-zero external force acts on a system of particles, it causes the centre of mass of the system to accelerate with acceleration a0 at any instant t. In such a case, the velocity of centre of mass of the system of particles is either v0 or zero.
APPEARS IN
संबंधित प्रश्न
You are waiting for a train on a railway platform. Your three-year-old niece is standing on your iron trunk containing the luggage. Why does the trunk not recoil as she jumps off on the platform?
A collision experiment is done on a horizontal table kept in an elevator. Do you expect a change in the result if the elevator is accelerated up or down because of the noninertial character of the frame?
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 makes a difference whether the cage is completely closed or it has rods to let air pass?
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.
Seven homogeneous bricks, each of length L, are arranged as shown in figure. Each brick is displaced with respect to the one in contact by L/10. Find the x-coordinate fo the centre of mass relative to the origin shown.
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?
Find the ratio of the linear momenta of two particles of masses 1.0 kg and 4.0 kg if their kinetic energies are equal.
During a heavy rain, hailstones of average size 1.0 cm in diameter fall with an average speed of 20 m/s. Suppose 2000 hailstones strike every square meter of a 10 m × 10 m roof perpendicularly in one second and assume that the hailstones do not rebound. Calculate the average force exerted by the falling hailstones on the roof. Density of a hailstone is 900 kg/m3.
In an elastic collision
Two persons each of mass m are standing at the two extremes of a railroad car of mass M resting on a smooth track(In the following figure). The person on left jumps to the left with a horizontal speed u with respect to the state of the car before the jump. Thereafter, the other person jumps to the right, again with the same horizontal speed u with respect to the state of the car before his jump. Find the velocity of the car after both the persons have jumped off.
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?
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.]
The centre of mass of a system of particles does not depend upon, ______
Two particles P and Q of mass 1 kg and 3 kg respectively start moving towards each other from rest under mutual attraction. What is the velocity of their center of mass?
The centre of mass of a system of two particles divides the distance between them ______.
The ratio of weights of a man inside a lift when it is stationary and when it is going down with a uniform acceleration 'a' is 3 : 2. The value of 'a' will be ______.
(a< g, g = acceleration due to gravity)
Which of the following statements are correct?
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.)
- Torque τ caused by F about z axis is along `-hatk`.
- Torque τ′ caused by F about z′ axis is along `-hatk`.
- Torque τ caused by F about z axis is greater in magnitude than that about z axis.
- Total torque is given be τ = τ + τ′.
The mass per unit length of a non-uniform rod of length L varies as m = λx where λ is constant. The centre of mass of the rod will be at ______.