Effective spring constant for series-parallel spring combination

Steps:

• Springs P and Q (each k) in parallel: equivalent constant = k + k = 2k.
• This 2k in series with R (3k): 1/K_eq = 1/(2k) + 1/(3k) = (3 + 2)/(6k) = 5/(6k).
• Thus, K_eq = 6k/5.
• Total length increase ΔL = W / K_eq = 5W/(6k).

Why A is correct:

• ΔL = 5W/6k follows Hooke's law for the series-parallel effective constant.

Why the others are wrong:

• B: 3W/4k assumes incorrect series combination, like all three in series (1/K_eq = 3/k, ΔL = 3W/k, not matching).
• C: 7W/2k overestimates extension, possibly treating all in parallel (K_eq = 5k, ΔL = W/5k, inverted error).
• D: W/k ignores parallel effect, treating as single k spring.

Final answer: A