JEE Main · 2026 · 24 Jan 2026 · Shift 1 · Laws of Motion

A spring of force constant

15 N / m

is cut into two pieces. If the ratio of their length is

1 : 3

, then the force constant of smaller piece is ______

N / m

(A)15
(B)20
(C)60✓ Correct
(D)45

Answer: (C)

Solution

The force constant of a spring is inversely proportional to its natural length,

k ℓ = constant

. Cutting in the ratio

1 : 3

makes the smaller piece one-quarter of the original length,

ℓ /4

. Hence

k^{'} (\frac{ℓ}{4}) = k ℓ

, giving

k^{'} = 4 k = 4 \times 15 = 60

. The force constant of the smaller piece is

60 N/m

JEE Main · 2026 · 24 Jan 2026 · Shift 1 · Single correct option

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