The mass of a planet is $\frac{1}{9}$ of the mass of the Earth and its radius is half that of the Earth. If a body weighs $9 \ N$ on the Earth,its weight on the planet would be ........ $N$.

The angular speed of the Earth in $rad/s$,so that bodies on the equator may appear weightless is: [Use $g = 10\, m/s^2$ and the radius of the Earth $R = 6.4 \times 10^3\, km$]

The acceleration due to gravity becomes $\left(\frac{g}{2}\right)$ ($g =$ acceleration due to gravity on the surface of the earth) at a height equal to

$A$ planet has the same density as that of the Earth,and the universal gravitational constant $G$ is twice that of the Earth. The ratio of the acceleration due to gravity on the planet to that on the Earth is:

The mass of a spherical planet is $4$ times the mass of the earth, but its radius $(R)$ is the same as that of the earth. How much work is done in lifting a body of mass $5 \,kg$ through a distance of $2 \,m$ on the planet (in $\,J$)? (Take $g = 10 \,ms^{-2}$ for Earth)

If both the mass and the radius of the earth decrease by $1\%$,the value of the acceleration due to gravity will