Answer
(a) The gravitational force on the rock has a magnitude of $49N$.
The gravitational force on the pebble has a magnitude of $2.94\times10^{-3}N$.
(b) The acceleration of the rock and the pebble is $9.80m/s^2$
Work Step by Step
Mass of rock $(m_r)$ is $5kg$ and mass of pebble $(m_p)$ is $3\times10^{-4}kg$
(a) As we calculate the gravitational force upon these objects, we have the earth's mass $M_E=5.98\times10^{24}kg$, the earth's radius $r=6.38\times10^6m$ and $G=6.67\times10^{-11}Nm^2/kg^2$
$$W_r=G\frac{M_Em_r}{r^2}=49N$$ $$W_p=G\frac{M_Em_p}{r^2}=2.94\times10^{-3}N$$
(b) The acceleration of each object can be calculated using Newton's 2nd Law of Motion:
$$a_r=\frac{W_r}{m_r}=\frac{49}{5}=9.80m/s^2$$ $$a_p=\frac{W_p}{m_p}=\frac{2.94\times10^{-3}}{3\times10^{-4}}=9.80m/s^2$$
