Question

Two bodies, A and B of equal mass are kept at heights $20m$ and $30m$ respectively. Calculate the ratio of their potential energies.

Answer 1

Step 1; Given data and assumptions

Given data:

Height for body A $\left(h_1\right)=20m$

Height for body B $\left(h_2\right)=30m$

Assumptions:

Let,

The mass of each body be $\left(m\right)$

The potential energy of body A be $\left(U_1\right)$

The potential energy of body B be $\left(U_2\right)$

Acceleration due to gravity be $\left(g\right)$

Step 2: Formula used

According to the formula of gravitational potential energy

$$\begin{gathered} Potentialenergy=mass\times gravity\times height \\ U=mgh.......\left(a\right) \end{gathered}$$

Step 3: Calculating the potential energy of body A

$U_1=m\times g\times 20m........\left(b\right)$

Step 4: Calculating the potential energy of body B

$U_2=m\times g\times 30m........\left(c\right)$

Step 5: Finding the ratio of potential energies

On, dividing equation (b) by equation (c), we get

$$\begin{gathered} \frac{U_1}{U_2}=\frac{20mg}{30mg}=\frac{2}{3} \\ \frac{U_1}{U_2}=\frac{2}{3} \end{gathered}$$

Hence, the ratio of potential energies will be $2:3$.