A small block of mass 100 g is tied to a spring of spring constant 7.5 N/m and length 20 cm. The other end of spring fixed at a particular point A. If the block moves in a circular path on a smooth horizontal surface with constant angular velocity 5 rad/s about point A, then tension in the spring is

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(4) 0.75 N. Idea: the spring stretches, so the radius is not the natural length. The extension must satisfy both Hooke's law and the centripetal requirement at the stretched radius. Let the extension be x, so the radius is l₀+x: kx=mω²(l₀+x). mω²=0.1×25=2.5 N/m, and k=7.5 N/m: 7.5x=2.5(0.2+x)=0.5+2.5x 5x=0.5, so x=0.1 m. T=kx=7.5×0.1=0.75 N. The stretch is half the natural length again, so the radius is 0.3 m — treating it as 0.2 m gives 0.5 N, which is option (c) and the usual error.

A small block of mass 100 g is tied to a spring of spring constant 7.5 N/m and length 20 cm. The other end of spring fixed at a particular point A. If the block moves in a circular path on a smooth horizontal surface with constant angular velocity 5 rad/s about point A, then tension in the spring is

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Why the other options are wrong