A body of mass m=10 kg is attached to one end of a wire of length 0.3 m. The maximum angular speed (in rad s⁻¹) with which it can be rotated about its other end in a space station is . (Breaking stress of the wire =4.8×10⁷ N m⁻² and area of cross-section of the wire =10⁻² cm²)

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4. Given: m=10 kg, L=0.3 m, σ_b=4.8×10⁷ N m⁻², A=10⁻² cm²=10⁻⁶ m². In a space station the body is in free fall, so weight plays no part and the tension alone provides the centripetal force. The wire breaks at Tₘₐₓ=σ_b A=4.8×10⁷×10⁻⁶=48 N. Tₘₐₓ=mLωₘₐₓ², so ωₘₐₓ²=(48)/(10×0.3)=16 rad² s⁻². ωₘₐₓ=4 rad s⁻¹.

A body of mass m=10 kg is attached to one end of a wire of length 0.3 m. The maximum angular speed (in rad s⁻¹) with which it can be rotated about its other end in a space station is ______. (Breaking stress of the wire =4.8×10⁷ N m⁻² and area of cross-section of the wire =10⁻² cm²)

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