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

Height for the body (B)=$\left(h_1\right)=30m$

Assumptions:

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

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

Let the potential energy for the body (A) be $\left(U_1\right)$

And the potential energy for the body (B) be $\left(U_2\right)$

Step 2: Formula used

According to the formula of gravitational potential energy

$U=mgh.......\left(a\right)$

Step 3: Calculating the gravitational potential energy for body A

$$\begin{gathered} U_1=mg\left(20\right) \\ {U}_1=20mg.......\left(b\right) \end{gathered}$$

Step 4: Calculating the gravitational potential energy for body (B)

$$\begin{gathered} U_2=mg\left(30\right) \\ {U}_2=30mg.......\left(c\right) \end{gathered}$$

Step 5: Calculating the ratio of potential energies

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

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

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