A compression spring is made of music wire of $$20$$ mm diameter having a shear strength and shear modulus of $$800$$ MPa and $$80$$ GPa respectively. The mean coil diameter is $$20$$ mm, free length is $$40$$ mm and the number of active coils is $$10.$$ If the mean coil diameter is reduced to $$10$$ mm, the stiffness of the spring is approximately

A weighing machine consists of a 2 kg pan resting on a spring in this condition, with the pan resting on the spring, the length of the spring is 200 mm. When a mass of 20 kg is placed on the pan, the length of the spring becomes 100 mm. For the spring, the un-deformed length L and the spring constant K (stiffness) are