A string breaks if its tension exceeds 10 newtons. A stone of mass 250gm tied to this string of length 10cm is rotated in a horizontal circle. The maximum angular velocity of rotation can be:
Correct answer: A. 20rad/s
- A. 20rad/s
- B. 40rad/s
- C. 100rad/s
- D. 200rad/s
Explanation
The maximum angular velocity of rotation for the stone tied to the string is 20 rad/s. This value is obtained by equating the maximum tension allowed by the string to the centripetal force acting on the stone. Options B, C, and D are incorrect as they provide angular velocity values that do not align with the calculated result.To find the maximum angular velocity (ωmax), we set the centripetal force equal to the maximum tension the string can withstand (Tmax):Fc = mω2 rTmax = mωmax2 rRearrange the equation to solve for ωmax:mωmax2 = Tmax / (mr)ωmax = √(Tmax / (mr)Substitute the known values into the equation:ωmax = √(10 / (0.25 × 0.1))ωmax = √(10 / 0.025)ωmax= √400ωmax= 20 rad/s
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Rotational motion relates angular displacement, angular velocity and angular acceleration to linear displacement, tangential velocity and tangential acceleration through the radius. Questions use radians, v equals r omega and tangential acceleration, while distinguishing tangential velocity from centripetal acceleration and angular quantities from their linear counterparts.
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