14. a ball initially at rest rolls without slipping
an incline of height 'h'. what is the linear
speed of the ball when it rolls onto the
horizontal surface?
solution:

v = √(10gh/7)

Explanation:

Initial gravitational energy = final rotational energy + kinetic energy

PE = RE + KE

mgh = ½ Iω² + ½ mv²

For a solid sphere, I = ⅖ mr².

For rolling without slipping, ω = v/r.

mgh = ½ (⅖ mr²) (v/r)² + ½ mv²

mgh = ⅕ mv² + ½ mv²

mgh = 7/10 mv²

10/7 gh = v²

v = √(10gh/7)

answer: the metamorphic rocks are formed when they are exposed to high pressure and high temperatures. this happens when one of the earth's plates comes in contact with the other plate by traveling in opposite directions, straight into each other or slipping under one another. the friction that is caused by this activity results in   melting of rocks and when it cools they are known as metamorphic rocks. this process needs a controlled amount of pressure and temperature otherwise it may turn into magma.