Two equal masses of 1 kg each are connected by a spring of force constant 10 N/m and natural length 1 m. They rotate about their common centre of mass with angular speed 2 rad/s. If the spring extension is x and 100x=N, find N.
Physics · Circular Motion · centripital force and centrifugal force
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Question

Two equal masses of 1 kg each are connected by a spring of force constant 10 N/m and natural length 1 m. They rotate about their common centre of mass with angular speed 2 rad/s. If the spring extension is x and 100x=N, find N.

Physics · Circular Motion · centripital force and centrifugal force

G1 Physics · Accepted Answer

For two equal masses m=1 kg, each mass moves in a circle of radius L/2, where L=1+x is the stretched spring length. Spring force is kx. For either mass, kx = mω²(L/2). Thus 10x = 1×4×(1+x)/2 = 2(1+x). Hence 10x = 2+2x, so 8x=2 and x=1/4 m. Therefore 100x=25 and N=25.