In an old Sherlock Holmes movie, a **** kept a 12.5 cm long (mass 1 kg), in a 15 cm thick book (excluding thickness of the covers) with a spring trap. The spring has 25 turns each of 1 mm thickness. The spring is fixed at the back cover and the presses the spring to its maximum when the front cover is closed so that the turns touch each other. The design is such that if the book is held in front of the body and opened, the gets detached from the spring and hits the reader ( Sherlock Holmes in this case). Unstretched length of the spring is equal to thickness of the book. However, Sherlock Holmes was too smart and hence he opened the book in such a way that the flew vertically upwards. All the energy of the spring is given to the which just reached the ceiling, at a height of 5 m from the tip of the and got stuck there. Calculate the spring constant which satisfies the equation F = - kx.
(a) 160/9 N/mm
(b) 40/9 N/mm
(c) 40 N/mm
(d) 6.4 N/mm
