Question

The mass of the moon is 734$\times {10}^{20}kgandtheradiusis1.74\times {10}^6$m. the gravitational field strength at its surface is :

• A. $1.45Nk{g}^{-1}$
• B. $1.55Nk{g}^{-1}$
• C. $1.75Nk{g}^{-1}$
• D. $1.62Nk{g}^{-1}$

Answer 1

The correct option is D $1.62Nk{g}^{-1}$

The gravitational field strength at the surface of a spherical body is given by:

$g=\frac{GM}{R^2}$

where,

$G=6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}$ is the universal Gravitational constant,

$M$ is the mass of the body and

$R$ is the radius of the body.

For the Moon,

$M=734\times {10}^{20}kg$ and $R=1.74\times {10}^{6}m$.

Substituting these values in the above equation we get the gravitational field strength at the surface as:

$g=\frac{(6.67\times {10}^{-11})\cdot (734\times {10}^{20})}{(1.74\times {10}^6{)}^2}$

$g=1.62Nk{g}^{-1}$