Question

A block is acted upon by a force, which is inversely proportional to the distance covered (x). The work done will be proportional to(a) x(b) $x^{\frac{1}{2}}$(c) x²(d) None of these

Answer 1

since force is proportional to x

i.e. ma=kx where k is any constant

      mvdv/dx=kx

       vdv=k’xdx where k’=k/m

        on integrating we have 

         v2/2= k’x2/2

          v=k’x

         work done = change in kinetic energy

                         i.e. proportional to x2