Question

The planet in space with mass twice as that of
the Earth and a radius thrice as that of the Earth.
If the weight of a book is 90 N on the Earth,
what would be the weight on that planet?
​

Answer 1

Answer :- 20 N

$\bf\huge\underline{\underline{ Given :- }}$

• A planet has twice mass of earth .

• Radius as thrice as that of earth

• weight of a book at earth is 90 N

$\bf\huge\underline{\underline{ To \: Find:- }}$

• weight of book on that palnet

$\bf\huge\underline{\underline{ Answer :- }}$

• $\boxed{\bf g = \frac{GM}{r²} }$

• The value of g earth is 9.8 m/s² , ≈ 10 m/s²

• weight of that book = mass × g

• 90 = mass × 10

• mass = 9 kg

$\rule{10cm}{0.05cm}$

• Let mass of earth = M

• mass of that planet be 2M

• Let radius of earth = R

• radius of planet = 3R

$\rule{10cm}{0.00005cm}$

• $\red{\implies} \bf g = \frac{GM}{r²}$

• $\red{\implies} \bf g^{h} = \frac{G2M}{(3R)²}$

• $\red{\implies} \bf g^{h} = \frac{2GM}{9R²}$

• $\red{\implies} \bf g^{h} =\frac{2}{9} × \frac{GM}{R²}$

• $\red{\implies} \bf g^{h} = \frac{2}{9}× g$

$\rule{10cm}{0.05cm}$

• weight of that book =$\bf 9 × \frac{2}{9}× 10$

• $\red{\implies}$ weight of that book = $\bf 2× 10$

• $\red{\implies}$ weight of that book = 20 N

$\rule{10cm}{0.05cm}$