Question

A table has a heavy circular top of radius 1m and mass 20kg, placed on four light (considered massless) legs placed symmetrically on its circumference. The maximum mass that can be kept anywhere on the table without toppling it is close to

Answer 1

Answer: $m = 48.31 kg$

Explanation:

Given that,

Radius r = 1 m

Mass m = 20 kg

Let us consider the table to have four legs arranged in a square.

Using Pythagoras theorem,

The distance between any side of the square formed by legs

$d= \sqrt{1^{2}+1^{2}}$

$d = \sqrt{2}$

For balance condition,

Now, the maximum mass is

$mg\times1 = (mg+20kg)\times \dfrac{\sqrt2}{2}$

$2mg -mg\sqrt{2} = 20\sqrt{2}$

$m = \dfrac{20}{\sqrt{2}-1}\ kg$

$m = 48.31 kg$

Hence, the maximum mass is the $m = 48.31 kg$