A body of mass m is connected to a spring of length l and spring constant k. Now, the spring is cut into two pieces of lengths in the ratio 2:3 and connected as shown. The equivalent spring constant is 25k/x, find x.
Physics · Mixed Chapter
JEE Mains

Question

A body of mass m is connected to a spring of length l and spring constant k. Now, the spring is cut into two pieces of lengths in the ratio 2:3 and connected as shown. The equivalent spring constant is 25k/x, find x.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: For a uniform spring the spring constant varies inversely with length. The cut pieces have lengths 2l/5 and 3l/5. Step 2: Their constants are k₁=k·l/(2l/5)=5k/2 and k₂=k·l/(3l/5)=5k/3. Step 3: Both pieces connect the mass to fixed walls, so for a small horizontal displacement their restoring forces add: effective spring constant=k₁+k₂=(5/2+5/3)k=25k/6. Step 4: Given effective spring constant=25k/x, x=6. Answer: 6.