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Grade 12Mechanics

Q: find the speed of cylinder(intially at rest) after it has rolled down a height of h in an inclined plane of inclination theta.There is no slipping.I ve solved the question through energy conservation but my answer is not coming through work energy theorem.Pls solve dis through work energy.

aryan

10 Years agoGrade 12

1 Answer

Siva Rama Krishna Gudipudi

10 Years ago

first I will take it as a solid cylinder and after I will take it as a hollow cylinder since you have not mentioned it.

for a solid cylinder ,take the energy equation as ,

mgh=1/2I $\omega$ ²+1/2mv²

then mgh=3/4mv²

from this we get v= √[4/3gh]

and next we calculate for hollow cylinder,

take mgh=1/2l $\omega$ ²+1/2mv²

we get ,mgh=mv²

from this we get as v=√[gh]

hence you get the answer and here you should know the moment of inertia of solid and hollow cylinders,

moment of inertia of solid cylinder is 1/2mr²

moment of inertia of hollow cylinder is mr²

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