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Work Energy Theorem Application

The minimum i...

Question

The minimum initial speed of the bullet, if the block and the bullet are to successfully execute a complete ride on the loop, is:

A

3 \sqrt{g R}

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B

3 \sqrt{5 g R}

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C

5 \sqrt{g R}

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D

5 \sqrt{3 g R}

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Solution

The correct option is B $3 \sqrt{5 g R}$

When the bullet of mass ' $m$ ' hits the block of mass ' $2 m$ ', the total mass becomes $3 m$ . and we know that if a particle of any mass wants to complete a circle then it should have a minimum speed of $\sqrt{5 g R}$ . It means that bullet plus block mass system has a minimum velocity of $\sqrt{5 g R}$ at the lowermost point. Now, we can apply the law of conservation of linear momentum. we have
$m v_{0} = (m + 2 m) \sqrt{5 g R} \Rightarrow v_{0} = 3 \sqrt{5 g R}$

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