Question

The acceleration due to gravity on the planet A is 9 times the acceleration due to gravity on planet B. A man jumps to a height of 2m on the surface of A. What is the height of jump by the same person on the planet B.

• A. \(\frac 29 \ m\)
• B. \(18\  m\)
• C. \(6\  m\)
• D. \(\frac {2}{3 }\ m\)

Answer 1

The Correct Option is B

Let's solve the problem step by step:

1. g_A = 9 \times g_B, where g_A and g_B are the accelerations due to gravity on planets A and B, respectively.
2. We know the formula for the maximum height (h) reached during a jump is given by: h = \frac{v^2}{2g} where v is the initial velocity and g is the acceleration due to gravity.
3. For planet A, the man reaches a height of 2m: h_A = \frac{v^2}{2g_A} = 2 \text{ m}
4. Re-arranging the formula for initial velocity v, v^2 = 2 \times g_A \times h_A = 2 \times 9 \times g_B \times 2\text{ m} = 36 \times g_B \text{ m}
5. For planet B, using the same initial velocity v for the jump, the height h_B that can be achieved is: h_B = \frac{v^2}{2g_B} = \frac{36 \times g_B}{2 \times g_B} = 18 \text{ m}

After calculations, the height of the jump on planet B is 18 \text{ m}. Therefore, the correct answer is:

18 \text{ m}

Options:

• \(\frac{2}{9}\) m - Incorrect, as this value is too small.
• 18 m - Correct, as calculated.
• 6 m - Incorrect, as this does not match our calculated value.
• \(\frac{2}{3}\) m - Incorrect, as this value is also incorrect.