A spring of spring constant $5 \times 10^{3} \mathrm{~N/m}$ is stretched initially by 5 cm from the unstretched position. Then the work required to stretch it further by another 5 cm is
(1) $12.50 \mathrm{~N-m}$
(2) $18.75 \mathrm{~N-m}$
(3) $25.00 \mathrm{~N-m}$
(4) $6.25 \mathrm{~N-m}$

A body of mass 1 kg falls freely from a height of 100 m, on a platform of mass 3 kg which is mounted on a spring having spring constant $\mathrm { k } = 1.25 \times 10 ^ { 6 } \mathrm {~N} / \mathrm { m }$. The body sticks to the platform and the spring's maximum compression is found to be $x$. Given that $g = 10 \mathrm {~ms} ^ { - 2 }$, the value of x will be close to:
(1) 40 cm
(2) 4 cm
(3) 80 cm
(4) 8 cm

A block of mass '$m$' (as shown in figure) moving with kinetic energy $E$ compresses a spring through a distance 25 cm when, its speed is halved. The value of spring constant of used spring will be $nE$ N$^{-1}$ for $n =$ \_\_\_\_. [Figure]

A block is fastened to a horizontal spring. The block is pulled to a distance $x = 10 \mathrm {~cm}$ from its equilibrium position (at $x = 0$ ) on a frictionless surface from rest. The energy of the block at $x = 5 \mathrm {~cm}$ is 0.25 J . The spring constant of the spring is $\_\_\_\_$ $\mathrm { N } \mathrm { m } ^ { - 1 }$.