Question

For the cube-rod-sphere combination shown, the density of the material is uniform throughout the object. A thin rod of length, $d$, connects the centers of the two objects.
Where is the center of mass?

• A. Inside the cube
• B. Closer to the cube than to the sphere
• C. At the midpoint between the cube and the sphere
• D. Closer to the sphere than to the cube
• E. Inside the sphere

Answer 1

The correct option is C At the midpoint between the cube and the sphere

The centre of mass of the two body system (when both masses are equal) is given by ,

$x_{cm}=x_1+x_2/2$ ,

where $x_1,x_2$ are the distances of masses from origin respectively , let the first mass is at origin then ,

$x_1=0$ and $x_2=d$

where $d=$ distance between two masses ,

in the given diagram , the masses are equal therefore centre of mass will be ,

$x_{cm}=0+d/2=d/2$ ,

the location of CM is at the midpoint between the cube and sphere .