Question

A neutron star of mass 2×10^30 kg and radius 10 km rotates with a period of 0.02 seconds. What is its rotational kinetic energy?

a) 2.5 × 10^35 J
b) 5.0 × 10^35 J
c) 1.25 × 10^35 J
d) 1.0 × 10^35 J

Answer 1

To calculate the rotational kinetic energy of the neutron star, we need to use the formula for rotational kinetic energy and the moment of inertia for a solid sphere. Plugging in the given values, we can calculate the rotational kinetic energy of the neutron star.

Step-by-step explanation:

The rotational kinetic energy of the neutron star can be calculated using the formula:

Rotational Kinetic Energy = (1/2) * (moment of inertia) * (angular velocity)^2

To find the moment of inertia, we can use the formula for the moment of inertia of a solid sphere:

Moment of Inertia = (2/5) * (mass) * (radius)^2

Plugging in the given values:

Mass = 2×10^30 kg

Radius = 10 km = 10^4 m

Angular velocity = 2π / (0.02 s) = 314.16 rad/s

Using these values, we can calculate the rotational kinetic energy:

Rotational Kinetic Energy = (1/2) * (2/5) * (2×10^30 kg) * (10^4 m)^2 * (314.16 rad/s)^2

Solving this equation will give us the answer.