A planet has mass 1/10 of that of earth, while radius is 1/3 that of earth. If a person can throw a stone on earth surface to a height of 90m, then he will be able to throw the stone on that planet to a height.

The correct option is 100m.

To find the height to which a person can throw a stone on the planet, we need to compare the acceleration due to gravity on the planet with that on Earth.

Step 1: Formula for acceleration due to gravity
The acceleration due to gravity ($g$) on the surface of a celestial body of mass $M$ and radius $R$ is given by the formula:
$g=\frac{GM}{R^2}$
where $G$ is the universal gravitational constant.

Let the mass of Earth be $M_e$ and its radius be $R_e$. The acceleration due to gravity on Earth is:
$g_e=\frac{G{M}_e}{R_e^2}$

Step 2: Calculate gravity on the planet
For the planet, we are given:
Mass of the planet, $M_p=\frac{1}{10}{M}_e$
Radius of the planet, $R_p=\frac{1}{3}{R}_e$

Substituting these values into the formula for gravity on the planet ($g_p$):
$g_p=\frac{G{M}_p}{R_p^2}=\frac{G\left(\frac{M_e}{10}\right)}{{\left(\frac{R_e}{3}\right)}^2}$

Simplifying the expression:
$g_p=\frac{9}{10}\left(\frac{G{M}_e}{R_e^2}\right)=\frac{9}{10}{g}_e$

Step 3: Relationship between height and gravity
When a stone is thrown vertically upward with an initial velocity $u$, the maximum height $h$ it attains is given by the kinematic equation:
$h=\frac{u^2}{2g}$

Assuming the person throws the stone with the same initial velocity $u$ on both Earth and the planet, the height is inversely proportional to gravity:
$h\propto \frac{1}{g}$

Therefore, we can write the ratio of heights as:
$\frac{h_p}{h_e}=\frac{g_e}{g_p}$

Step 4: Calculate the height on the planet
Substitute the values of $h_e=90\text{m}$ and $g_p=\frac{9}{10}{g}_e$ into the ratio:
$\frac{h_p}{90}=\frac{g_e}{\frac{9}{10}{g}_e}=\frac{10}{9}$

Solving for $h_p$:
$h_p=90\times \frac{10}{9}=100\text{m}$

Thus, the person will be able to throw the stone to a height of 100m on that planet.