Solve the Problem $\mathrm { d }$ , That a Spring Is Compressed from Its Natural, Uncompressed

Multiple Choice

Solve the problem.
-The number of centimeters, $\mathrm { d }$ , that a spring is compressed from its natural, uncompressed position is given by the formula $\mathrm { d } = \sqrt { \frac { 2 \mathrm {~W} } { \mathrm { k } } }$ , where $\mathrm { W }$ is the number of joules of work done to move the spring and $\mathrm { k }$ is the spring constant. Solve this equation for W. Use the result to determine the work needed to move a spring 3 centimeters if it has a spring constant of $0.2$ .

A) $\mathrm { W } = \frac { \mathrm { d } ^ { 2 } \mathrm { k } } { 2 } ; 0.9$ joules
B) $\mathrm { W } = \frac { \mathrm { d } ^ { 2 } \mathrm { k } ^ { 2 } } { 4 } ; 0.1$ joules
C) $W = \frac { 2 d ^ { 2 } } { k } ; 90$ joules
D) $\mathrm { W } = 2 \mathrm {~d} ^ { 2 } \mathrm { k } ; 3.6$ joules