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? (A) (3v2/2g sin θ) (B) (v2/4g sin θ) (C) (3v2/g sin θ) (D) (3v2/4g sin θ)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/42e865f040103ac1b6dd5b01b9ae10c5-.png" /> Let the cylinder go up the plane upto a height h. Let M and R be the mass and radius of the cylinder respectively. According to law of conservation of mechanical energy, we get (1/2)Mv2 + (1/2) Iω2 = Mgh (1/2)Mv2 +(1/2)(MR2/2) ω2 = Mgh (∵ textFor a solid cylinder, I= (1/2)MR2) (1/2)Mv2 +(1/4)MR2ω2 = Mgh (1/2)Mv2+(1/4)Mv2 = Mgh (∵ v= Rω) (3/4)Mv2 = Mgh h= (3v2/4 g) ...(i) Let s be distance travelled by the cylinder up the plane.Then sin θ = (h/s) or s = (h/sin θ) = (3 v2/4 g sin θ) (Using(i))

Q. 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?

$\frac{3 v ^{2}}{2 g s in θ}$

$\frac{v ^{2}}{4 g s in θ}$

$\frac{3 v ^{2}}{g s in θ}$

$\frac{3 v ^{2}}{4 g s in θ}$

Q. 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?

2gsinθ3v2​

4gsinθv2​

gsinθ3v2​

4gsinθ3v2​

Q. 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?

$\frac{3 v ^{2}}{2 g s in θ}$

$\frac{v ^{2}}{4 g s in θ}$

$\frac{3 v ^{2}}{g s in θ}$

$\frac{3 v ^{2}}{4 g s in θ}$