A metal wire of length 0.5 m and cross-sectional area 10⁻⁴ m² has a breaking stress of 5×10⁸ N m⁻². A block of 10 kg is attached at one end of the wire and is rotated in a horizontal circle. The maximum linear velocity of the block will be m s⁻¹.

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50. Given: L=0.5 m (the radius of the circle), A=10⁻⁴ m², σ_b=5×10⁸ N m⁻², m=10 kg. The wire snaps when its tension reaches Tₘₐₓ=σ_b A=5×10⁸×10⁻⁴=5×10⁴ N. In a horizontal circle the tension alone is the centripetal force, so Tₘₐₓ=(mvₘₐₓ²)/L. vₘₐₓ²=(TₘₐₓL)/m=(5×10⁴×0.5)/(10)=2500 m² s⁻². vₘₐₓ=50 m s⁻¹.

A metal wire of length 0.5 m and cross-sectional area 10⁻⁴ m² has a breaking stress of 5×10⁸ N m⁻². A block of 10 kg is attached at one end of the wire and is rotated in a horizontal circle. The maximum linear velocity of the block will be ______ m s⁻¹.

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