Question

four uniform solid cubes of edge 10 cm, 20 cm, 30 cm and 40 cm are kept on the ground , touching each other in order . locate centre of mass of their system .​

Answer 1

Answer:

65 cm from the edge.

Step-by-step explanation:

See the attached diagram.

The volume of 10 cm cube is 1000 cm³

Now, the weight is proportional to volume as the density is constant.

So, the weight of 10 cm cube is 1000x (say)

The volume of 20 cm cube is 8000 cm³

So, the weight of 20 cm cube is 8000x (say)

The volume of 30 cm cube is 27000 cm³

So, the weight of 30 cm cube is 27000x (say)

The volume of 40 cm cube is 64000 cm³

So, the weight of 40 cm cube is 64000x (say)

Now, from the diagram, the weight of 10 cm cube acts through a point A' which is 5 cm distant from the edge of the cube O.

Hence, OA'= 5cm.

Similarly, if the weight of the 20cm cube passes through B' then OB'=20 cm.

Again, if the weight of the 30cm cube passes through C' then OC'=45 cm.

Again, if the weight of the 40cm cube passes through D' then OD'=80 cm.

If the center of mass of all the cubes passes through a point which is d cm from O, then

d=$\frac{5*1000x+20*8000x+45*27000x+80*64000x}{1000x+8000x+27000x+64000x}$

⇒ d=$\frac{6500000x}{100000x}$

⇒ d= 65 cm.

Therefore, the center of mass of the system passes through 65 cm distance from the edge of the 10 cm cube.