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 .

Step-by-step solution

Spring force constant is inversely proportional to length: k 1 L So kL = constant for a given spring material and structure. Original spring: k = 15 N/m, length = L . Smaller piece has length L 4 (since length ratio is 1:3, smaller is 1 4 of total). For smaller piece: k₁ L 4 = 15 L k₁ = 15 4 = 60 N/m