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Question: A solid cube of edge 'a' is molten and moulded in eight identical small solid cubes and are placed o...

A solid cube of 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 bottom cube on the same horizontal plane on which big cube was placed, then the vertical shift in centre of mass is-

A

3a2\frac{3a}{2}

B

2a

C

5a2\frac{5a}{2}

D

3a

Answer

3a2\frac{3a}{2}

Explanation

Solution

Final hight of centre of mass

= 4l (where 6mu 6mu8l3=a3⇒ 6mu 6mu 6mu 6mu 6mul=a2)\left( \begin{aligned} & where\mspace{6mu}\mspace{6mu} 8\mathcal{l}^{3} = a^{3} \\ & \Rightarrow \mathcal{\mspace{6mu}\mspace{6mu}\mspace{6mu}\mspace{6mu}\mspace{6mu} l} = \frac{a}{2} \end{aligned} \right)

Initial height of centre of mass = a2\frac{a}{2}

\ Dh = 4l – a2\frac{a}{2} = 2a –a2\frac{a}{2} = 3a2\frac{3a}{2}