An abstract sculpture consists of a ball (radius r = 76 cm) resting on top of a cube (each side l = 200 cm long). the ball and the cube are made of the same material of uniform density; there are no hollow spaces inside them. the bottom face of the cube rests on a horizontal floor. how high is the sculpture’s center of mass above the floor? answer in units of cm.

132.9 cm

Explanation:

Data provided in the question:

Radius of the basll = 76 cm = 0.76 m

Side of the box = 200 cm = 2 m

Density of the ball and cube are equal

let the density be 'D'

Now,

Mass of ball, M = Volume × Density

=  × D

= × D

= 1.838D

Mass of cube, m = L³ × D

= 2³ × D

= 8D

Thus,

center of mass, y = [ My₁ + my₂ ] ÷ [M + m]

here,

y₁ = center of mass of ball with respect to floor

as the center mass of sphere lies at the center of the sphere

= Length of cube + radius of sphere

= 2 + 0.76

= 2.76 m

y₂ = Center of mass of cube = = 1 m

Thus,

y = [ ( 1.838D × 2.76 ) + (8D × 1 ) ] ÷ [1.838D + 8D]

= 13.07288D ÷ 9.838D

= 1.329 m

or

= 132.9 cm

0.11 m/s and 0.28 m/s should be correct

the skeletons of most mammals reach a certain size and then stop growing. however, many animals, including some mammals, keep growing throughout their lives. kangaroos, for example, just keep growing and growing until they die. also, the longer an animal lives the greater the chance it might catch some deadly disease.