Question

Two $20g$ worms climb over a $10cm$ high, very thin wall. One worm is thin and $20cm$ long the other is fat and only $10cm$ long. What is the ratio of the potential energy ($w.r.t.$ the base of wall) of the thin worm as compared to that of the fat worm when each is half way over the top of the wall as shown?

• A. $1:1$
• B. $2:1$
• C. $2:3$
• D. $1:2$

Answer 1

The correct option is C $2:3$

Given: $m=20g,H=10cm$

In case $I$
The height of centre of mass of worm from ground$h_1=5cm$ for left half part So total potential energy will be

$U_1=0.02\times 10\times 0.05=0.01J$

In case $II$ The height of centre of mass of $2^{nd}$ worm from ground for left part

$h_2=5+\frac{5}{2}=\frac{15}{2}cm$

So total potential energy will be

$U_2=0.02\times 10\times 0.075=0.015J$

$\therefore \frac{U_1}{U_2}=\frac{0.01}{0.015}=\frac{2}{3}$