A newly discovered spherical planet has a mass 48 times that of the...

Let the mass, volume, and radius of the Earth be $M$, $V$, and $R$ respectively.

For the new planet, mass $M' = 48M$ and volume $V' = 64V$.

Since the volume of a sphere is proportional to the cube of its radius, $V' = 64V \Rightarrow R'^3 = 64R^3 \Rightarrow R' = 4R$.

The acceleration due to gravity on the surface of a planet is given by $g = \dfrac{GM}{R^2}$.

For the new planet, $g' = \dfrac{GM'}{R'^2} = \dfrac{G(48M)}{(4R)^2} = \dfrac{48GM}{16R^2} = 3\dfrac{GM}{R^2} = 3g$.

The weight of the block on Earth is $W = mg$.

The weight of the block on the new planet is $W' = mg' = m(3g) = 3W$.

Answer: $3W$