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Question

A bob is suspended from a crane by a cable of length $$5m$$. The crane and load are moving at a constant speed $$v_{0}$$. The crane is stopped by a bumper and the bob on the cable swings out an angle of $$60^{\circ}$$. Find the initial speed $$v_{0}.(g=9.8 m/s^{2})$$

237417_b16cb54503674fdfb9d1873f2863fa46.png


A
2ms1
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B
3ms1
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C
5ms1
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D
7ms1
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Solution

The correct option is D $$7 ms^{-1}$$
By using conservation of energy, from the initial point to the highest point
$$\frac { 1 }{ 2 } m{ { v }_{ 0 } }^{ 2 }=mgl(1-cos{ 60 }^{ 0 })$$ 
$$\Rightarrow { v }_{ 0 }=\sqrt { 2gl(1-cos{ 60 }^{ 0 }) } =\sqrt { gl } =\sqrt { 50 } =7m/s$$

Physics

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