Ram and Shyam each of mass 45kg reach the fourth floor of a building in time 4 sec and 5 sec respectively. The ratio of their inertia is :

Options

A. `4:5`
B. `5:4`
C. `1:1`
D. Information is incomplete

Explanation

To solve the problem, we need to find the ratio of inertia between Ram and Shyam, given that both have the same mass. Here’s a step-by-step solution:

### Step 1: Understand the Concept of Inertia
Inertia is a property of matter that quantifies its resistance to changes in motion. The inertia of an object is directly proportional to its mass. Therefore, we can say:
\[ \text{Inertia} \propto \text{Mass} \]

### Step 2: Define the Mass of Ram and Shyam
According to the problem, both Ram and Shyam have the same mass:
- Mass of Ram (M_R) = 45 kg
- Mass of Shyam (M_S) = 45 kg

### Step 3: Write the Inertia for Ram and Shyam
Let’s denote the inertia of Ram as \( I_R \) and the inertia of Shyam as \( I_S \). Since inertia is proportional to mass, we can express their inertia as:
- \( I_R \propto M_R \)
- \( I_S \propto M_S \)

### Step 4: Calculate the Ratio of Their Inertia
Now, we can find the ratio of their inertia:
\[ \frac{I_R}{I_S} = \frac{M_R}{M_S} \]

Substituting the values:
\[ \frac{I_R}{I_S} = \frac{45 \, \text{kg}}{45 \, \text{kg}} = 1 \]

### Step 5: Express the Ratio
The ratio of their inertia can be expressed as:
\[ I_R : I_S = 1 : 1 \]

### Conclusion
Thus, the ratio of the inertia of Ram and Shyam is \( 1 : 1 \).

### Final Answer
The correct answer is option 3: \( 1 : 1 \).

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