a point mass (m) is located at (0,a) where should th 2m mass be kept ,so that centre of mass lies at origin?

A point object of mass m is kept at (a, 0) along x-axis. What mass should be kept at (-3a,0), so that centre of mass lies at origin ?

An equilateral triangular plate of mass 4m of side a is kept as shown. Consider two cases: (i) a point mass 4m is placed at the vertex P of the plate (ii) a point mass m is placed at the vertex R of the plate. In both cases the x-coordinate of centre of mass remains the same. Then x coordinate of centre of mass of the plate is

Centre of mass of three particles of masses 1 kg, 2 kg and 3 kg lies at the point (1,2,3) and centre of mass of another system of particles 3 kg and 2 kg lies at the point (-1, 3, -2) . Where should we put a particle of mass 5 kg so that the centre of mass of entire system lies at the centre of mass of first system ?

The coordinates of the centre of mass of a system of three particles of mass 1g,2g and 3g are (2,2,2). Where should a fourth particle of mass 4 g be positioned so that the centre of mass of the four particle system is at the origin of the three-dimensional coordinate system ?

Three particles of masses m , m and 4kg are kept at a verticals of triangle ABC . Coordinates of A , B and C are (1,2) , (3,2) and (-2,-2) respectively such that the centre of mass lies at origin. Find the value of mass m . Hint. x_(cm)=(sum_(i-1)^(3)m_(i)x_(i))/(sum_(i=1)^(3)m_(i)) , y_(cm)=(sum_(i=1)^(3)m_(i)y_(i))/(sum_(i=1)^(3)m_(i))

Three particles of masses m , m and 4kg are kept at a verticals of triangle ABC . Coordinates of A , B and C are (1,2) , (3,2) and (-2,-2) respectively such that the centre of mass lies at origin. Find the value of mass m . Hint. x_(cm)=(sum_(i-1)^(3)m_(i)x_(i))/(sum_(i=1)^(3)m_(i)) , y_(cm)=(sum_(i=1)^(3)m_(i)y_(i))/(sum_(i=1)^(3)m_(i))

Two rods of equal lengths(l) and equal mass M are kept along x and y axis respectively such that their centre of mass lie at origin. The moment of inertia about an line y = x, is

Consider a system of two particles having masses 2kg and 5 kg the particle of mass 2 kg is pushed towards the centre of mass of particles through a distance 5 m,by what distance would particle of mass 5kg move so as to keep the centre of mass of particles at the original position?

A point mass m is placed inside a spherical shell of radius R and mass M at a distance R/2 form the centre of the shell. The gravitational force exerted by the shell on the point mass is

There are two masses m_1 and m_2 placed at a distance l apart. Let the centre of mass of this system is at a point named C. If m_1 is displaced by l_1 towards C and m_2 is displaced by l_2 away from C. Find the distance, from C where new centre of mass will be located.