A body of mass `m kg` lifted by a man to a height of one metre in `30 sec` . Another mass lifted the same mass to the same height in `60 sec` . The work done by then are them are in the ratio.

Options

A. `1:2`
B. `1:1`
C. `2:1`
D. `4:1`

Answer

To solve the problem, we need to determine the work done by a man lifting a mass to a height of 1 meter in two different time intervals. The key point to note is that the work done is independent of the time taken to lift the mass.

### Step-by-Step Solution:

1. **Understanding Work Done**:
Work done (W) in lifting an object is given by the formula:
\[ W = m \cdot g \cdot h \]
where:
- \( m \) = mass of the object (in kg)
- \( g \) = acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \))
- \( h \) = height (in meters)

2. **Calculate Work Done in Both Cases**:
- In both scenarios, the height \( h \) is 1 meter.
- Therefore, the work done in both cases can be calculated as:
\[ W_1 = m \cdot g \cdot 1 = mg \quad \text{(for the first case, lifted in 30 seconds)} \]
\[ W_2 = m \cdot g \cdot 1 = mg \quad \text{(for the second case, lifted in 60 seconds)} \]

3. **Comparing Work Done**:
- Since both \( W_1 \) and \( W_2 \) are equal to \( mg \), we can conclude:
\[ W_1 = W_2 \]

4. **Finding the Ratio**:
- The ratio of work done by the man in both cases is:
\[ \text{Ratio} = \frac{W_1}{W_2} = \frac{mg}{mg} = 1 \]
- Therefore, the ratio of work done is \( 1:1 \).

### Final Answer:
The work done by the man in both cases is in the ratio \( 1:1 \).