Advertisements
Advertisements
Question
Find out the centre of mass for the given geometrical structures.
a) Equilateral triangle
b) Cylinder
c) Square
Solution
a)
b)
c)
(a) For an equilateral triangle, the center of mass lies at its centroid.
(b) For the cylinder, center of mass lies at its geometrical center.
(c) For square, the center of mass lies at the point where the diagonals meet.
APPEARS IN
RELATED QUESTIONS
If all the particles of a system lie in X-Y plane, is it necessary that the centre of mass be in X-Y plane?
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?
A circular plate of diameter d is kept in contact with a square plate of edge d as show in figure. The density of the material and the thickness are same everywhere. The centre of mass of the composite system will be 
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.
Mr. Verma (50 kg) and Mr. Mathur (60 kg) are sitting at the two extremes of a 4 m long boat (40 kg) standing still in water. To discuss a mechanics problem, they come to the middle of the boat. Neglecting friction with water, how far does the boat move on the water during the process?
A block of mass 2.0 kg moving 2.0 m/s collides head on with another block of equal mass kept at rest. (a) Find the maximum possible loss in kinetic energy due to the collision. (b) If he actual loss in kinetic energy is half of this maximum, find the coefficient of restitution.
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.]
Three equal masses each of 50 g, are placed at the corners of a right angled isosceles triangle whose two equal sides are 5 cm each. The position of the centre of mass of the system is ____________.
A mass of 1kg is suspended by a string. It is first lifted up with an acceleration of 4.9 m/s2 and then lowered down with same acceleration. The ratio of tensions in the string in the two cases, respectively is g = 9.8 m/s2 ______.
Centre of mass is a point ______.
