Question

There are two mass less spring A and B of spring constant $K_A$ and $K_B$ respectively $K_A>K_B$ . If $W_{A}and{W}_B$ be denoted as work done on A andwork done on B respectively, then

• A. if they are compressed to same distance,
• B. if they are compressed by same force (upto equilibrium state)
• C. if they are compressed by same distance,
• D. if they are compressed by same force (upto equilibrium state)

Answer 1

Answer: (A), (B)

The correct options are
A

if they are compressed to same distance,

B

if they are compressed by same force (upto equilibrium state)

$W_A=\frac{1}{2}{K}_A{x}^2$;$W_B=\frac{1}{2}{K}_B{x}^2$ $\because K_A>K_B\Rightarrow W_A>W_B$

If the springs are compressed by same force

$F=K_A{x}_A=K_B{x}_B;x_A=\frac{F}{K_A};x_B=\frac{F}{K_B};$

$\frac{W_A}{W_B}$ $=\frac{\frac{1}{2}{K}_A\frac{F^2}{K_A^2}}{\frac{1}{2}{K}_B\frac{F^2}{K_B^2}}=\frac{K_B}{K_A}$

$W_A<W_B$