A body of mass m = 1 kg is dropped form a height h = 40 cm on a horizontal plateform fixed to one end of an elastic spring , the other being fixed to a base, as shown in Fig. As a result the springs is sompressed by an amouont x=10cm. What is the force cosntan of the spring Take `g=10ms^(2)`

Options

A. `600Nm^(-1)`
B. ` 800Nm^(-1)`
C. ` 1000Nm^(-1)`
D. ` 1200Nm^(-1)`

Answer

C

Explanation

Since the platform is depressed by an amount x, the total work done on the spring is mg `(h +x)`. This work is stored in the spring in the form of potential energy ` (1)/(2) kx^(2)`. Equating the two, we have
`(1)/(2) kx^(2) = mg (h +x) or k = (2mg (h + x))/(x^(2)) = 1000 Nm^(-1)`