Question

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 the space station is (Breaking stress of wire = 4.8 × 10⁷ Nm^-2 and the area of cross-section of the wire = 10^-2 cm²) is ______.

पर्याय

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Answer 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 the space station is (Breaking stress of wire = 4.8 × 10⁷ Nm^-2 and the area of cross-section of the wire = 10^-2 cm²) is 4.

Explanation:

T = `mlomega^2`

`sigma = T/A = (mlomega^2)/A`

`(mlomega^2)/A ≤ 48 xx 10^7 ⇒ omega^2 ≤ ((48 xx 10^7)A)/(ml)`

⇒ `omega^2 ≤ ((48 xx 10^7)(10^-6))/(10 xx 3) = 16 ⇒ omega_{max}` = 4 rad/s