A small bob tied at one end of a thin string of length $$1$$ m is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio $$5$$:$$1$$. The velocity of the bob at the highest position $$is_________$$ $$m/s$$. (Take$$ $$g=10m/s2)

Question

A small bob tied at one end of a thin string of length $$1$$ m is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio $$5$$:$$1$$. The velocity of the bob at the highest position $$is_________$$ $$m/s$$. (Take$$ $$g=10m/s2)

Infinity Learn · Accepted Answer

At bottom, let say speed is v∴$$Tmax=mv2L+mgAs$$ bob goes up, its speed decreases to uLoss in $$KE$$ $$=$$ Gain in $$PE$$⇒$$12mv2$$−$$12mu2=mg(2L)$$⇒$$u2=v2$$−$$4gL$$ At top, tension is minimum, ⇒$$Tmin=mu2L$$−$$mg=mv2$$−$$4gLL$$−$$mg=mv2L$$−$$5mg$$ Given :$$TmaxTmin=51$$⇒$$mv2L+mgmv2L$$−$$5mg=51$$⇒$$v2=132gL$$ Thus, $$u2=v2$$−$$4gL=132gL$$−$$4gL=52gL$$⇒$$u=5$$×$$10$$×$$12=5m/s$$

Conservation of mechanical energy

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A small bob tied at one end of a thin string of length 1 m is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio 5:1. The velocity of the bob at the highest position is_________ m/s. (Take $g = 10 m / s^{2}$ )

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Conservation of mechanical energy

Remember concepts with our Masterclasses.

A small bob tied at one end of a thin string of length 1 m is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio 5:1. The velocity of the bob at the highest position is_________ m/s. (Take g=10m/s2)

Ready to Test Your Skills?

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A small bob tied at one end of a thin string of length 1 m is describing a vertical circle so that the maximum and minimum tension in the string are in the ratio 5:1. The velocity of the bob at the highest position is_________ m/s. (Take $g = 10 m / s^{2}$ )