Saved Bookmarks
| 1. |
State Boyle's law. Derive it on the basis of the kinetic theory of an ideal gas. |
|
Answer» Solution :For a circulary symmetric rigid body, starting from rest and rolling down an INCLINED plane without slipping, its speed after a VERTICAL displacement h is `v=sqrt((2gh)/(1+(I//MR^(2))))""`….(1) where M, R and I are respectively the mass, radius and moment of inertia of the body. (i) For a ring (or a thin-walled hollow CYLINDER), `I=MR^(2)""`...(2) `:. (I)/(MR^(2))=1` `:. v=sqrt((2gh)/(1+(I)/(MR^(2))))""`....(3) (ii) For a solid cylinder (or a disc), `I=(1)/(2)MR^(2)""`....(4) `:. (I)/(MR^(2))=(1)/(2)` `:. v=sqrt((2gh)/(1+(I)/(MR^(2))))=sqrt((2gh)/(1+(1)/(2)))=sqrt((3)/(4)gh)""`......(5) (iii) For a solid SPHERE, `I=(2)/(5)MR^(2)""`....(6) `:. (I)/(MR^(2))=(2)/(5)` `:. v=sqrt((2gh)/(1+(I)/(MR^(2))))=sqrt((2gh)/(1+(2)/(5)))=sqrt((10)/(7)gh)""`......(7) |
|