An object with low moment of inertia will acquire less rotational kinetic energy and more translational kinetic energy (moves faster down the ramp) than an object with higher moment of inertia.

Moment of inertia depends on how close to the object's center of mass its mass is concentrated. An object with more of its mass close to the center will have lower moment of inertia, and subsequently more translational kinetic energy. The solid sphere has lowest moment of inertia, then the disk, and then the hollow sphere, thus the solid sphere reaches the end first, then the disk, and finally the hollow sphere.

Since the ramp is frictionless all the energy in the system is conserved. All the potential energy is converted into kinetic energy.

The potential energy is given by: 

The kinetic energy formula is:

Since all of the potential energy is converted to kinetic energy we can solve for velocity.

There are two types of units: base units and derived units. Base units are a set of units from which all other units are derived, whereas derived units are the units derived from base units.

There are six main base units: meters, kilogram, second, Ampere, Kelvin, moles, and candela (unit for luminous intensity). The rest of the units are classified as derived units and will contain a combination of these base units. The SI units for the four measurements listed in question are as follows:

Mass: 

Volume:  (Liters)

Weight:  (Newtons)

Density: 

This means that volume, weight, and density are derived units, whereas mass is a base unit. 

Derived units are derived from the six base units. A derived unit usually contains multiple base units that are combined by using multiplication and/or division; addition and subtraction of base units is not performed to obtain derived units.

The SI unit for force is Newtons. Newtons written in base units is ; therefore, units for force is always a derived unit. A unit can be either a derived unit or a base unit, but it can never be both. Recall that there are only six base units and numerous derived units; therefore, there are more derived units than base units. 

The SI base unit for time is seconds. Hours are derived by multiplying seconds by sixty. Hours are not a base unit.

Recall that the mass of a substance is usually measured in kilograms (), which is a type of base unit. Moles () is a unit used to measure the amount of substance. Moles are also a type of base unit; therefore, both the unit for mass () and the unit for amount of substance () are measures of base units. 

Scalar quantities are those that can be described with magnitude only, as opposed to vectors, which include both magnitude and direction components. Distance, speed, and time are all scalars. Displacement is not a scalar, as it involves both the distance and the direction moved from a starting point. Velocity also includes a direction component, and is therefore a vector quantity.

A vector quantity has has both magnitude and direction. By definition, only velocity satisfies these criteria.

Distance, angle, and speed have magnitude, but no direction.

The answer to this question lies within Newton's third law: for every action, there is an equal and opposite reaction. If the large ball applies a  force on the smaller ball, the smaller ball will apply a  force on the large ball in the opposite (negative) direction.

This is a conservation of energy question. The event is the collision. The initial energy can be calculated by gravitational potential energy:

The final total energy must be the same. The energy of the scattered pieces must add to 

When the rope is around the pulley, the acceleration is slower due to internal friction, thus the initial acceleration of the platform would be lower. Once the platform was in free fall, however, the acceleration due to gravity is constant at 9.8 m/s²; thus, the final acceleration of the platform is the same in both scenarios.