A body of mass m is from surface of the earth projected vertically upwards with a velocity such that it rises to a height of 20 m. If the same body is projected with same velocity from a planet density is `(1)/(4)` th of density of earth and radius is `(1)/(2)` of that of Earth, then find the height to which the body will rise on the planet.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the problem and the given data
We have a body of mass \( m \) that is projected vertically upwards from the surface of the Earth with a certain initial velocity \( u \). It reaches a height of \( h_E = 20 \, \text{m} \) on Earth. We need to find the height \( h_P \) to which the same body will rise when projected with the same initial velocity from a planet that has a density of \( \frac{1}{4} \) that of Earth and a radius of \( \frac{1}{2} \) that of Earth.

### Step 2: Use the kinematic equation
The kinematic equation for vertical motion is given by:
\[
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