A rod of length L is placed along the X-axis between `x=0 and x=L`. The linear density (mass/length) `rho` of the rod varies with the distance x from the origin as `rho=a+bx. ` a.) Find the SI units of a and b b.) Find the mass of the rod in terms of a,b, and L.

Answer

A, B

Explanation

`rho=mass/lengtyh =a+bx, a. S.I. uit of 'a'=kg/m, S.I. unit of 'b' = kg/m^2`, (from principle of homogeneity of dimensions) b. Let us consider a sma element of length dx at a distance x from the origin as shown in the ure dm=mass of the element, =rho dx, =(a+dx)dx, mass of the rod = int dm, =int^L_0 (a+dx)dx, =[ax+(bx^2)/2]^2_0, =2L+(BL^2)/2`