Question

Four bricks, each of length $l$, are put on the top of one another in such a way that part of each extends beyond the one beneath. Pick the correct statement(s) in reference to the maximum value of overhanging length(in terms of $l$), such that the system is in equilibrium

• A. The top brick overhangs the one below by $\frac{l}{2}$
• B. The second brick from top over hangs the one below by $\frac{l}{4}$.
• C. The third brick from top overhangs the bottom one by $\frac{l}{6}$
• D. The total overhanging length on the edge of the bottom brick is $\left(\frac{11}{12}\right)l$.

Answer 1

Answer: (A), (B), (C), (D)

The total overhanging length on the edge of the bottom brick is $\left(\frac{11}{12}\right)l$.

Let the weight of each brick be $W$ and length $l$.

As bricks are homogeneous, the centre of gravity of each brick must be at the midpoint. Therefore, the topmost brick will be in equilibrium if its centre of gravity lies at the edge of brick below it, i.e., second brick.

Thus the topmost brick can have maximum equilibrium extension of $\frac{l}{2}$

$C_1$ is the centre of mass of the top two bricks which lies on the edge of the third brick.
$C_2$ is the centre of mass of the top three bricks which lies on the edge of the fourth brick.
Thus, the maximum overhanging length to top from the edge of bottom brick is
$\frac{l}{2}+\frac{l}{4}+\frac{l}{6}=\frac{11}{12}l$