Gives the speed v versus time t for a 0.500 kg object of radius 6.00 cm that rolls smoothly down a 30° ramp. The scale on the velocity axis is set by vs = 4.0 m/s. What is the rotational inertia of the object?

Rotational inertia of the object is given as

Explanation:

As we know that the acceleration of the object on inclined plane is given as

now we know that velocity at any instant of time is given as

now we know that if the graph between velocity and time is given then the slope of the graph will be same as acceleration

so here we have

now from the graph slope of the graph is given as

now rotational inertia is given as

Neptune is the eighth planet from the sun. it was the first planet to get its existence predicted by  mathematical calculations  before it was actually seen through a telescope on sept. 23, 1846. irregularities in the orbit of  uranus  led french astronomer alexis bouvard to suggest that the gravitational pull from another celestial body might be responsible. german astronomer johann galle then relied on subsequent calculations to   spot neptune via telescope. previously, astronomer galileo galilei sketched the planet, but he mistook it for a star due to its slow motion. in accordance with all the other planets seen in the sky, this new world was given a name from greek and roman mythology — neptune, the roman god of the sea.