A 1 kg block is dropped from a point 1.2 m above an initially uncompressed vertical spring of force constant 200 N/m. Take g = 10 m/s². If the maximum compression is N/10 m, find N.
Physics · Work , Power and Energy · conservation of mechanical energy
JEE Mains NEET JEE Advanced

Question

A 1 kg block is dropped from a point 1.2 m above an initially uncompressed vertical spring of force constant 200 N/m. Take g = 10 m/s². If the maximum compression is N/10 m, find N.

G1 Physics · Accepted Answer

At maximum compression x, the block has lost gravitational potential mg(1.2+x), stored as spring energy ½kx². So 10(1.2+x)=100x² ⇒ 100x²−10x−12=0 ⇒ x=0.4 m. Hence N=4.