Question

A planet has a mass 20%more
than that of earth. and radius is 20%
less than earth. Then find the acceleration
due to gravity of plant
PRIO​

Answer 1

SoluTion :

✴ Given :-

▪ A planet has a mass 20% more than that of earth and radius is 20% less than earth.

✴ To Find :-

▪ Acceleration due to gravity of planet.

✴ Formula :-

✈ Formula of acceleration due to gravity of a planet is given by...

$\bigstar\:\boxed{\sf{\pink{\large{g=\dfrac{GM}{R^2}}}}}$

• g denotes gravitational acceleration
• G denotes gravitational constant
• M denotes mass of planet
• R denotes radius of planet

✴ Calculation :-

• Radius of earth = R
• Radius of planet = R'
• Mass of earth = M
• Mass of planet = M'
• Gravitational acc. of earth = g
• Gravitational acc. of planet =g'

$\circ\sf\:R'=R-\dfrac{20R}{100}=\dfrac{4R}{5}\\ \\ \circ\sf\:M'=M+\dfrac{20M}{100}=\dfrac{6M}{5}\\ \\ \mapsto\sf\:\dfrac{g'}{g}=\dfrac{M'}{{R'}^2}\times \dfrac{R^2}{M}\\ \\ \mapsto\sf\:\dfrac{g'}{9.8}=\dfrac{6}{5}\times (\dfrac{5}{4})^2\\ \\ \mapsto\sf\:\dfrac{g'}{9.8}=1.875\\ \\ \mapsto\:\boxed{\sf{\large{\orange{g'=18.375\:ms^{-2}}}}}$