Question

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-​

Answer 1

$\bigstar$ Answer $\bigstar$

$\checkmark$ Given:

A planet has mass 1/10 of that of earth

Radius is 1/3 of that of earth

A person can throw  a stone to a height of 90 m on earth

$\checkmark$ To Find:

To what height he will be able to throw the stone on that planet

$\checkmark$ Solution:

We know that,

$\star$ Acceleration due to Gravity (g)

$\red{\boxed{\rm g=\dfrac{GM}{R^{2}} }}$

From this we can understand that,

$\green{\implies \rm g \propto M}$

$\blue{\implies \rm g \propto \dfrac{1}{R^{2}} }$

Here,

G is a constant

G = 6.673×10⁻¹¹ N m² kg⁻²

Let us consider,

p = Planet

e = Earth

Therefore,

$\green{\rm \dfrac{g_{p}}{g_{e}}=\dfrac{M_{p}}{M_{e}} \times \left(\dfrac{R_{e}}{R_{p}}\right)^{2}}$

Given that,

$\blue{\rm \implies \dfrac{M_{p}}{M_{e}}=\dfrac{1}{10} }$

$\green{\rm \implies \dfrac{R_{e}}{R_{p}}=\dfrac{3}{1} }$

By Substituting,

We get,

$\pink{\implies \rm \dfrac{g_{p}}{g_{e}}=\dfrac{1}{10} \times \left(\dfrac{3}{1}\right)^{2}}$

$\green{\implies \rm \dfrac{g_{p}}{g_{e}}=\dfrac{1}{10} \times \dfrac{9}{1}}$

$\red{\implies \rm \dfrac{g_{p}}{g_{e}}=\dfrac{9}{10}}$

Given that,

A person can throw  a stone to a height of 90 m on earth

Then,

$\star$ Height (H)

$\orange{\boxed{\rm H=\dfrac{u^{2}}{2g} }}$

From this we can understand that,

$\green{\rm \implies H \propto \dfrac{1}{g} }$

Therefore,

$\pink{\rm \dfrac{H_{p}}{H_{e}} = \dfrac{g_{e}}{g_{p}} }$

Given that,

$\blue{\implies \rm H_{e}=90\ m}$

And. We found out that,

$\red{\implies \rm \dfrac{g_{p}}{g_{e}}=\dfrac{9}{10}}$

Therefore,

$\blue{\implies \rm \dfrac{g_{e}}{g_{p}}=\dfrac{10}{9}}$

By Substituting,

We get,

$\pink{\implies \rm \dfrac{H_{p}}{90} = \dfrac{10}{9} \ m}$

$\blue{\rm \implies H_{p}=\dfrac{10}{9} \times 90 \ m }$

$\red{\rm \implies H_{p}=10 \times 10 \ m }$

$\orange{\rm \implies H_{p}=100 \ m }$

Hence,

He will be able to throw the stone to a height 100 m in that planet

Answer 2

Explanation:

g constant on earth that is g= GM/R

g constant on planet that is g ^1=3GM/10R

relation between then g^1= 3g/10

Now energy remains constant

Hence, mg×90= m×3g×h/100

we get h=300m.

hope you understood

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