A solid cylinder rolls up an inclined plane of inclination θ with an initial velocity v. How far does the cylinder go up the plane?

Question

A solid cylinder rolls up an inclined plane of inclination θ with an initial velocity v. How far does the cylinder go up the plane?

Infinity Learn · Accepted Answer

Let the cylinder go up the plane upto a height h. Let M and R be the mass and radius of cylinder respectively. According to law of conservation of mechanical energy, we get            $$12Mv2+12I$$ω$$2$$ $$=$$ Mgh $$($$∵ For a solid cylinder, I $$=$$ $$12MR2)$$           $$12Mv2+14MR2$$ω$$2$$ $$=$$ Mgh             $$12Mv2+14Mv2$$ $$=$$ Mgh     $$($$∵ v $$=$$ Rω$$)$$             $$34Mv2$$ $$=$$ Mgh              h $$=$$ $$3v24gLet$$ s be distance travelled by the cylinder up the plane.       $$s=hSin$$ θ$$=3v24gSin$$ θ

A solid cylinder rolls up an inclined plane of inclination $θ$ with an initial velocity v. How far does the cylinder go up the plane?

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