A uniform rectangular thin sheet ABCD of mass M has length a and breadth b, as shown in the figure. If the shaded portion HBGO is cut-off, the coordinates of the centre of mass of the remaining portion will be:
The position vector of the centre of mass vec rcm of an asymmetric uniform bar of negligible area of cross section as shown in figure is :
Which of the following statements are correct?
(A) Centre of mass of a body always coincides with the centre of gravity of the body.
(B) Centre of mass of a body is the point at which the total gravitational torque on the body is zero.
(C) A couple on a body produce both translational and rotational motion in a body.
(D) Mechanical advantage greater than one means that small effort can be used to lift a large load.
Three particles of masses 50 g, 100 g and 150 g are placed at the vertices of an equilateral triangle of side 1 m (as shown in the figure). The (x, y) coordinates of the centre of mass will be:
Two particles which are initially at rest, move towards each other under the action of their internal attraction. If their speeds are u and 2 at any instant, then the speed of centre of mass of the system will be :
An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If AB = BC and the angle made by AB with download vertical is 0, then
Two particles A and B (both initially at rest) start moving towards each other under a mutual force of attraction. At the instant when the speed of A is v and the speed of B is 2v,the speed of the center of mass is
