Saved Bookmarks
| 1. |
A rod of length L and cross section area A has variable density according to the relation `rho (x)=rho_(0)+kx` for `0 le x le L/2` and `rho(x)=2x^(2)` for `L/2 le x le L` where `rho_(0)` and k are constants. Find the mass of the rod. |
|
Answer» Correct Answer - `((7L^(3))/12+rho_(0)L/2+(kL^(2))/8)A` `M_(1)=underset(0)overset(L//2)(int)A(rho_(0)+kx)dx=(rho_(0) L/2+(kL^(2))/8)A` `M_(2)=underset(L//2)overset(L)(int)A(2x^(2)dx)=2/3[L^(3)-L^(3)/8]=(14L^(3))/24 A` `M_("total")=M_(1)+M_(2)=((14L^(3))/24+rho_(0)L/2+(kL^(2))/8)A` |
|