A space ship of mass $$2 \times 10^{4} \mathrm{~kg}$$ is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the space ship in the orbit to overcome the gravitational pull will be (if $$g=10 \mathrm{~m} / \mathrm{s}^{2}$$ and radius of earth $$=6400 \mathrm{~km}$$ ):

When vector $$\vec{A}=2 \hat{i}+3 \hat{j}+2 \hat{k}$$ is subtracted from vector $$\overrightarrow{\mathrm{B}}$$, it gives a vector equal to $$2 \hat{j}$$. Then the magnitude of vector $$\overrightarrow{\mathrm{B}}$$ will be :

If force (F), velocity (V) and time (T) are considered as fundamental physical quantity, then dimensional formula of density will be :

If $$\mathrm{V}$$ is the gravitational potential due to sphere of uniform density on it's surface, then it's value at the center of sphere will be:-