Four small spheres are positioned on a horizontal tabletop and connected by light

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

Four small spheres are positioned on a horizontal tabletop and connected by light, rigid rods that do not interfere with motion. Three of the spheres each have mass

M

and are located at the coordinates

(a,0)

(-a,0)

, and

(0,b)

in an

xy

-plane. The fourth sphere has mass

2M

and is positioned at

(0,-b)

. Assume

a>0

and

b>0

. (a) Identify any symmetry lines of the mass distribution and explain how they simplify locating the center of mass. (b) Derive expressions for the

x

– and

y

–coordinates of the overall center of mass in terms of

a

and

b

. (c) For

a = 0.20\,\text{m}

and

b = 0.15\,\text{m}

, compute the numerical coordinates of the center of mass.

Related theory

Centre of Mass
Systems of Particles & Centre of Mass

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