Question

If g1 and g2 denote acceleration due to gravity on the surface of the earth and on a planet respectively, whose mass and radius are twice that of the earth,then

1) g1 =2g2
2) g2=2g1
3) g1=g2
4) g1=2g2^2

Answer 1

$\red{HEY\:BUDDY!!}$

HERE'S THE ANSWER...

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♠️ We know Acceleration due to gravity

=> $\large{ g\:=G ×M\: \div R^2}$

⏺️G is universal gravitational constant

⏺️R is radius of Earth

⏺️M is mass of Earth

▶️ According to question

⏺️ Mass of Planet = 2 M

⏺️ Radius of planet = 2 R

♠️ Now acceleration due to gravity on earth

=> $\bold{ g_{1}\:=\:GM \div R^2}$

♠️Now acceleration due to gravity on planet

=> $\bold{ g_{2}\:=\:G(2M) \div (2R)^2}$

=> $\bold{ g_{2}\:=\:2GM \div 4R^2}$

=> $\bold{ g_{2}\:=\:GM \div 2R^2}$

=> $\bold{ g_{2}\:=\:g_{1} \div 2}$

=> $\boxed{ g_{1}\:=\: 2g_{2}}$

♠️ So option ( 1 ) is correct..

HOPE HELPED..

$\red{JAI \:HIND..}$

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Answer 2

g = GM/R^2

g2 = 2GM / (2R)^2

g2 = GM/2R^2

Now putting the value

g2 = g1 / 2

g 1 = 2g2


so option 1 is right