If a person can jump on the earth surface upto a height 2 m . His jump on a satellite where acceleration due to gravity is `1.96 m //s^2` will be -

Options

A. 5 m
B. 10 m
C. 20 m
D. 2 m

Answer

To solve the problem step by step, we can use the relationship between the maximum height a person can jump and the acceleration due to gravity.

### Step 1: Understand the relationship between height and gravity
The maximum height \( h \) that a person can jump is inversely proportional to the acceleration due to gravity \( g \). This can be expressed as:
\[ \frac{h'}{h} = \frac{g}{g'} \]
where:
- \( h' \) is the height the person can jump on the satellite,
- \( h \) is the height the person can jump on Earth (2 m),
- \( g \) is the acceleration due to gravity on Earth (approximately \( 9.8 \, \text{m/s}^2 \)),
- \( g' \) is the acceleration due to gravity on the satellite (\( 1.96 \, \text{m/s}^2 \)).

### Step 2: Substitute known values into the equation
We know:
- \( h = 2 \, \text{m} \)
- \( g = 9.8 \, \text{m/s}^2 \)
- \( g' = 1.96 \, \text{m/s}^2 \)

Substituting these values into the equation gives:
\[ \frac{h'}{2} = \frac{9.8}{1.96} \]

### Step 3: Calculate the ratio
Now, calculate the right-hand side:
\[ \frac{9.8}{1.96} = 5 \]
This means:
\[ \frac{h'}{2} = 5 \]

### Step 4: Solve for \( h' \)
To find \( h' \), multiply both sides by 2:
\[ h' = 5 \times 2 = 10 \, \text{m} \]

### Conclusion
Thus, the height the person can jump on the satellite is:
\[ \boxed{10 \, \text{m}} \]