A body of mass m and radius R rolling horizontally without slipping at a speed v climbs aramp to a height⡱ぉㄘ⡲〴 . The rolling body can be

It seems like your question got cut off. However, I can start explaining the concept of a body of mass m and radius R rolling horizontally without slipping at a speed v.

1. First, we need to understand the concept of rolling without slipping. This means that the point of the body in contact with the surface is momentarily at rest. This is a condition for pure rolling motion.

2. The kinetic energy of a rolling body is the sum of the translational kinetic energy and the rotational kinetic energy. The translational kinetic energy can be given by (1/2)mv^2 and the rotational kinetic energy by (1/2)Iω^2, where I is the moment of inertia and ω is the angular velocity.

3. For a body rolling without slipping, v = Rω. Therefore, the total kinetic energy can be written as (1/2)mR^2ω^2 + (1/2)Iω^2.

4. If the body climbs a ramp to a height h, it will lose kinetic energy and gain potential energy. The potential energy gained is mgh.

5. By conservation of energy, the initial kinetic energy of the body should be equal to the final potential energy. Therefore, (1/2)mR^2ω^2 + (1/2)Iω^2 = mgh.

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