A planet in a distant solar system is $$10$$ times more massive than the earth and its radius is $$10$$ times smaller. Given that the escape velocity from the earth is $$11\,\,km\,{s^{ - 1}},$$ the escape velocity from the surface of the planet would be

If $${g_E}$$ and $${g_M}$$ are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan's oil drop experiment could be performed on the two surfaces, one will find the ratio
$${{electro\,\,ch\arg e\,\,on\,\,the\,\,moon} \over {electronic\,\,ch\arg e\,\,on\,\,the\,\,earth}}\,\,to\,be$$

A particle of mass $$10$$ $$g$$ is kept on the surface of a uniform sphere of mass $$100$$ $$kg$$ and radius $$10$$ $$cm.$$ Find the work to be done against the gravitational force between them to take the particle far away from the sphere (you may take $$G$$ $$ = 6.67 \times {10^{ - 11}}\,\,N{m^2}/k{g^2}$$)

Average density of the earth