Question

The sun's mass is about 2×1030kg and its radius is 7×105km . it's rotational period is about 28days . if the sun should collapse into a white dwarf of radius 6500km what would its new period of rotation be? assume that no mass is lost in the process and that the sun before and after the collapse can be modeled as a uniform density sphere.

a) 14 days
b) 7 days
c) 56 days
d) 28 days

Answer 1

The new rotational period of the Sun after collapsing into a white dwarf with a radius of 6500 km will be 28 days.

Step-by-step explanation:

To find the new rotational period of the Sun after it collapses into a white dwarf with a radius of 6500 km, we can use the principle of conservation of angular momentum.

The angular momentum of an object is given by the product of its moment of inertia and its angular velocity. Since we are assuming no mass is lost in the collapse and the Sun can be modeled as a uniform density sphere, the moment of inertia remains the same before and after the collapse.

Therefore, we can set up the equation:

initial moment of inertia x initial rotational period = final moment of inertia x final rotational period

The moment of inertia of a sphere is given by 2/5 * mass * radius^2.

Plugging in the given values, 2/5 * (2 × 10³0 kg) * (7 × 105 km)^2 = 2/5 * (2 × 10³0 kg) * (6500 km)^2, we can solve for the final rotational period. The answer is d) 28 days.