Question

There are two massless springs A and B of spring constant $K_A$ and $K_B$ respectively and $K_A>K_B$. If $W_A$ and $W_B$ be denoted as work done on A and work done on B respectively, then

• A. If they are compressed to same distance, $W_A>W_B$
• B. If they are compressed by same force (upto equilibrium state) $W_A<W_B$
• C. If they are compressed by same distance, $W_A<W_B$
• D. If they are compressed by same force (upto equilibrium state) $W_A>W_B$

Answer 1

Answer: (A), (B)

The correct options are
A If they are compressed to same distance, $W_A>W_B$
B If they are compressed by same force (upto equilibrium state) $W_A<W_B$

If the springs are compressed to same amount: $W_A=\frac{1}{2}{K}_A{x}^2;W_B=\frac{1}{2}{K}_B{x}^2\because K_A>K_B\Rightarrow W_A>W_B$

If the springs are compressed by same force.
$F=K_A{x}_A=K_B{x}_B;x_A=\frac{F}{K_A};x_B=\frac{F}{K_B};\frac{W_A}{W_B}=\frac{\frac{1}{2}{K}_A.\frac{F^2}{K_A^2}}{\frac{1}{2}{K}_B\frac{F^2}{K_B^2}}=\frac{K_B}{K_A}<1$
Hence, $W_A<W_B$