The radii of two planets are respectively R₁ and R₂ and their densities are respectively \(\rho\)₁ and \(\rho\)₂ the ratio of the accelerations due to gravity at their surface is ________

(a)

\({ g }_{ 1 }:{ g }_{ 2 }=\frac { { \rho }_{ 1 } }{ { R }_{ 1 }^{ 2 } } :\frac { { \rho }_{ 2 } }{ { R }_{ 2 }^{ 2 } } \)

(b)

g₁:g₂=R₁R₂:\(\rho\)₁ \(\rho\)₂ 

(c)

g₁:g₂=R₁\(\rho\)₂:R₂ \(\rho\)₁

(d)

g₁:g₂=R₁\(\rho\)₁:R₂ \(\rho\)₂ 

The acceleration due to gravity near the surface of a planet of radius R and density d is proportional to ____________.

(a)

\(\frac{d}{R^2}\)

(b)

dR²

(c)

dR

(d)

\(\frac{d}{R}\)

The acceleration of a body due to the attraction of the Earth (radius R) at a distance 2R from the surface of the Earth is __________.

(a)

\(\frac{g}{9}\)

(b)

\(\frac{g}{3}\)

(c)

\(\frac{g}{4}\)

(d)

9

If density of Earth increased 4 times and its radius becomes half of then out weight will be ________.

(a)

four times its present value

(b)

doubled

(c)

remains same

(d)

halved

The radius of the Earth is 6400 km and g = 10 ms^-2 in order that a body of 5 kg weights zero at the equator, the angular speed of the Earth is _______ rad R^-1

(a)

\(\frac{1}{80}\)

(b)

\(\frac{1}{400}\)

(c)

\(\frac{1}{800}\)

(d)

\(\frac{1}{600}\)