A \(12\,\mathrm{kg}\) object is in a gravitational field of magnitude \(4.0\,\mathrm{N\,kg^{-1}}\). Find its weight magnitude.

An object has mass \(20\,\mathrm{kg}\). If the local gravitational field halves, what happens to its mass and weight?

A \(75\,\mathrm{kg}\) explorer has weight \(255\,\mathrm{N}\) on a moon. Find the moon's local gravitational field magnitude.

A \(25\,\mathrm{kg}\) payload is outside a spherical body of mass \(7.0\times10^{22}\,\mathrm{kg}\), at \(2.0\times10^6\,\mathrm{m}\) from its center. Find the payload's weight magnitude. Use \(G=6.67\times10^{-11}\,\mathrm{N\,m^2\,kg^{-2}}\).

An object has weight \(W_R\) at radius \(R\) from a spherical planet. Find its weight at radius \(2R\).

Two probes have masses \(m\) and \(3m\). They are at radii \(R\) and \(2R\) from the same spherical source. Find the ratio of their weight magnitudes \(W_{3m,2R}/W_{m,R}\).

At what height above the surface of a spherical planet of radius \(R\) is an object's weight half its surface weight?

A \(5.0\,\mathrm{kg}\) object is in a local gravitational field \(\vec g=(-2.0\hat{\imath}-7.0\hat{\jmath})\,\mathrm{N\,kg^{-1}}\). Find its weight vector and magnitude.

A \(50\,\mathrm{kg}\) lander has weight \(300\,\mathrm{N}\) at radius \(8.0\times10^6\,\mathrm{m}\) from a spherical planet's center. Infer the planet mass. Use \(G=6.67\times10^{-11}\,\mathrm{N\,m^2\,kg^{-2}}\).

A body of radius \(R\) has surface weight \(W_s\). Derive the height \(h\) above the surface at which the weight has fallen by a fraction \(p\), so \(W=(1-p)W_s\). State the allowed range of \(p\).