# There are two planets A and B in the solar system. The acceleration due to gravity on planet A is 11 times the acceleration due to gravity on planet B

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There are two planets A and B in the solar system. The acceleration due to gravity on planet A is 11 times the acceleration due to gravity on planet B. If a man jumps to a height of 3 m on planet A, what is the height of jump by the same person on planet B?

1. 4 m
2. 12 m
3. 27 m
4. 33 m

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Correct Answer - Option 4 : 33 m

The correct answer is option 4) i.e. 33 m

CONCEPT:

Kinematic equations of motion:

• These equations define the relationship between initial velocity u, final velocity v, time t, and displacement s of an object with respect to its motion in uniform acceleration a.
• Following are the three kinematic equations for uniformly accelerated motion:

⇒ v = u + at

⇒ s = ut + 0.5at2

⇒ v2 - u2 = 2as

CALCULATION:

Given that:

gA =11gB      ----(1)

Height of jump on planet A, hA = 3 m

Height of jump on planet b = hB

Using the equation of kinematics, v2 - u2 = 2gh

When the man jumps, his final velocity v = 0, and the acceleration due to gravity is negative.

⇒ - u2 = 2(-g)h

$⇒ g = \frac{u^2}{2h}$

Therefore, $g_A = \frac{u^2}{2h_A}$ and $g_B = \frac{u^2}{2h_B}$      ----(2)

From (1) and (2),

$\Rightarrow \frac{u^2}{2h_A} = 11\frac{u^2}{2h_B}$

$\Rightarrow h_B = 11h_A = 11 \times 3 = 33\: m$

The height of the jump by the same person on planet B is 33 m.