A solid cube of the edge a is molten and moulded in eight identical small solid cubes and are placed on one other on a straight line with the edge of the bottom cube on the same horizontal plane on which big cube was placed, then the vertical shift in the centre of mass is

Question

A solid cube of the edge a is molten and moulded in eight identical small solid cubes and are placed on one other on a straight line with the edge of the bottom cube on the same horizontal plane on which big cube was placed, then the vertical shift in the centre of mass is (A) (3 a/2) (B) 2a (C) (5 a/2) (D) 3a

Tardigrade Admin · Accepted Answer

Initial height of centre of mass =(a/2) keeping volume same, before and after 8 L3 = a3 ⇒ L = (a/2) (side of samller cubes) new height of center of mass = 4 L = 2 a Δ h = 2 a - (a/2) = (3/2) a

Q. A solid cube of the edge $a$ is molten and moulded in eight identical small solid cubes and are placed on one other on a straight line with the edge of the bottom cube on the same horizontal plane on which big cube was placed, then the vertical shift in the centre of mass is

$\frac{3 a}{2}$

$2 a$

$\frac{5 a}{2}$

$3 a$

$I ni t ia l h e i g h t o f ce n t re o f ma ss = \frac{a}{2}$
keeping volume same, before and after
$8 L^{3} = a^{3}$
$\Rightarrow L = \frac{a}{2}$ (side of samller cubes)
new height of center of mass $= 4 L = 2 a$
$Δ h = 2 a - \frac{a}{2} = \frac{3}{2} a$

Q. A solid cube of the edge a is molten and moulded in eight identical small solid cubes and are placed on one other on a straight line with the edge of the bottom cube on the same horizontal plane on which big cube was placed, then the vertical shift in the centre of mass is

23a​

2a

25a​

3a