Question

Two rods,'A' and 'B', of the same Weight and equal length, have different thickness. A boy, while playing with them on a beach,held them vertically on the surface of Sand as shown in the figure. Which one. of them Will sink less? Explain.

Answer 1

if lengths are equal along with their weights , then they will also have same diameter means same area of cross section.
recall pressure.
that is force per unit area.
force is same for both as their weights.
So when they will fall the area heading the sand will be different for one rod it will be the area of that small cross section (circle)
but for the second one which is horizontally falling ,it's area corresponding to length ( looks like a rectangle) will head the sand.
The area is first case(vertical rod) is small as compared to second rod( horizontal).
Implies that the pressure exerted by that small area of vertical rod compared to horizontal rod is more on sand as follows by force per unit area means if area is small pressure will be ore.
so the vertical rod will sink in sand more as compared to horizontal rod.