If the length of a thin uniform rod is ' $L$ ' and the radius of gyration of the rod about an axis perpendicular to its length and passing through one end is $K$, then $K: L=$

A thin uniform wire of mass ' $m$ ' and linear density ' $\rho$ ' is bent in the form of a circular ring. The moment of inertia of the ring about a tangent parallel to its diameter is ' $m$ '

A solid sphere and a thin uniform circular disc of same radius are rolling down an inclined plane without slipping. If the acceleration of the sphere is $3 \mathrm{~ms}^{-2}$, then the acceleration of the disc is

A balance is made using a uniform metre scale of mass 100 g and two plates each of mass 200 g fixed at the two ends of the scale and the balance is pivoted at 45 cm mark of the scale. The error when 300 g weight is placed in the plate at 0 cm to weigh vegetables placed in the plate at 100 cm is