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A ball of mass 0.5 kg is attached to a l...

A ball of mass 0.5 kg is attached to a light string of length 2m. The ball is whirled on la horizontal smooth surface is a circle of rdius 2 m as shown in fig. If the string can withstand tension up to 100 N, what is the maximum speed at which the bal can be whirled.

Text Solution

Verified by Experts

A stronger cord can whirl the ball faster before the string breaks. Also more massive the ball, probability of the string breaking at same speed is also very high.
Calculations: Only radial force is acting on the ball so we need to write only one equation `fsumF_(r)=mv_("max")^(2)//r`.

Furthermore, the maximum speed the ball can attain corresponding to the maximum tension that the string can withstand:
`T_("max")=(mv_("max")^(2))/r`
Solve for v
`v_("max")=sqrt((T_("max")r)/m)=sqrt(((100N)(2m))/(0.5 kg))=20m/s`
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