Question

a solid cylinder rolls up an inclined plane of inclination theta with an initial velocity v.how far does the cylinder goes up the plane​

Answer 1

Explanation:

Rotations of cylinder × curved surface area of cylinder

This will give you the answer.

Answer 2

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+12Iω2=Mgh

12Mv2+12MR2/2ω2=Mgh

(because For a solid cylinder, I=12MR2)

12Mv2+14MR2/ω2=Mgh

12Mv2+14Mv2=Mgh (∵v=Rω)

34Mv2=Mgh

h=3v24g ...(i)

Let s be distance travelled by the cylinder up the plane.

sinθhsor s=hsinθ=3v2/4gsinθ (Using (i)).

Explanation: