Two bodies of equal weight are kept at heights of h and 1.5 h respectively. The ratio of their P.E. is

Options

A. `3:2`
B. `2:3`
C. `1:1`
D. none of these

Answer

To find the ratio of potential energy (P.E.) of two bodies kept at different heights, we can follow these steps:

### Step 1: Understand the formula for Potential Energy
The potential energy (P.E.) of an object at height \( h \) is given by the formula:
\[ P.E. = mgh \]
where:
- \( m \) is the mass of the object,
- \( g \) is the acceleration due to gravity,
- \( h \) is the height above the reference point.

### Step 2: Identify the heights of the two bodies
We have two bodies:
- Body 1 is at height \( h \).
- Body 2 is at height \( 1.5h \).

### Step 3: Calculate the Potential Energy for both bodies
1. For Body 1 at height \( h \):
\[ P.E. (u_1) = mgh \]

2. For Body 2 at height \( 1.5h \):
\[ P.E. (u_2) = mg(1.5h) = 1.5mgh \]

### Step 4: Find the ratio of their Potential Energies
To find the ratio of the potential energies \( u_1 \) and \( u_2 \):
\[ \frac{u_1}{u_2} = \frac{mgh}{1.5mgh} \]

### Step 5: Simplify the ratio
The \( mgh \) terms cancel out:
\[ \frac{u_1}{u_2} = \frac{1}{1.5} = \frac{1}{\frac{3}{2}} = \frac{2}{3} \]

### Step 6: State the final ratio
Thus, the ratio of the potential energies of the two bodies is:
\[ \text{Ratio of } P.E. = 2 : 3 \]