Question

Four identical plates of mass $M$ and length $L$ are placed on one another on the table so as to produce the maximum overhang as shown in the figure. The maximum total overhang will be:

• A. $\frac{3L}{4}$
• B. $\frac{24L}{25}$
• C. $\frac{25L}{24}$
• D. $\frac{4L}{3}$

Answer 1

Answer: (C)

$\frac{25L}{24}$

If we take the displacement of the whole system to be x. So, when the four identical plates are placed one upon the other in such a manner that it will produce maximum overhang. Then each plates center of gravity must remain constant.

So, if the mass of the plates are M and length L.

So, Mx=M(L/2-x)

which on solving we will get the value of x=L/4.

Again for the n number blocks we will have

M(L/2 - xn) = M(n-1)xn

which on solving we will get L/2n.

So, for the 4 blocks we will get L/2,L/4,L/6,L/8 which will be 24L/25.