Question

- Mars has about 1/10th as much mass as the earth
and half as great a diameter. The acceleration of falling body on Mars in ms- is about (acceleration
due to gravity on earth = 9.8 ms)
(a) 1.96
(b) 3.92
(c) 4.9
(d) 9.8

Answer 1

We may recall the relation between the weight of the body of constant mass m and the gravitational force of attraction between the body and a planet of mass M and radius R.

$\quad$

$mg=\dfrac {GMm}{R^2}$

$\quad$

Since G is a constant, this implies the relation given below.

$\quad$

$g\propto\dfrac {M}{R^2}$

$\quad$

Then we form the equation,

$\quad$

$\dfrac {g_M}{g_E}=\dfrac {M_M}{M_E}\left (\dfrac {R_E}{R_M}\right)^2\\\\\\\dfrac {g_M}{g_E}=\dfrac {M_M}{M_E}\left (\dfrac {2R_E}{2R_M}\right)^2\\\\\\\dfrac {g_M}{g_E}=\dfrac {M_M}{M_E}\left (\dfrac {D_E}{D_M}\right)^2\\\\\\g_M=g_E\cdot\dfrac {M_M}{M_E}\left (\dfrac {D_E}{D_M}\right)^2$

$\quad$

Now, given,

$\quad$

$g_E=9.8\ ms^{-2}\\\\\\\dfrac {M_M}{M_E}=\dfrac {1}{10}\\\\\\\dfrac {D_M}{D_E}=\dfrac {1}{2}\quad\implies\quad\left (\dfrac {D_E}{D_M}\right)^2=4$

$\quad$

Then,

$\quad$

$g_M=9.8\times\dfrac {1}{10}\times 4\\\\\\\underline {\underline {g_M=3.92\ ms^{-2}}}$

Answer 2

Answer: (a) 1.96

Explanation: