Question

The following spring block systems having same mass of the block and same spring constants were stretched or compressed to different lengths (x) and released. Match the following:

• A. (1)-(i), (2) - (ii),(3) - (iii)
• B. (1)-(i), (2) - (i), (3) - (iii)
• C. (1)-(i), (2) - (ii), (3) - (i)
• D. None of these

Answer 1

The correct option is C

(1)-(i), (2) - (ii), (3) - (i)

On compressing or stretching the spring by amount x, the work done on it is equal to $\frac{1}{2}k{x}^2$ This gets stored as the total energy of the system.

For (1) x=$\frac{A}{2}$,T.E=$\frac{1}{2}k{\left(\frac{A}{2}\right)}^2=\frac{1}{8}K{A}^2$

For (2) $x=A_1$,T.E=$\frac{1}{2}k{A}^2$

FOr (3) $x=\frac{A}{2}$,T.E=$\frac{1}{2}k{\left(\frac{A}{2}\right)}^2=\frac{1}{8}K{A}^2$

Option (c) is correct !