A pendulum consists of a wooden bob of mass `M` and length `l`. A bullet of mass `m` is fired towards the pendulum with a speed `v`. The bullet emerges immediately out of the bob from the other side with a speed of `v//2` and the bob starts rising. Assume no loss of mass of bob takes place due to penetration. If the bob stops where the string becomes horizontal then `v` isA. `(2M)/m sqrt(3gl)`B. `(2M)/msqrt(5gl)`C. `(2M)/msqrt(gl)`D. `(2M)/msqrt(2gl)`

A pendulum consists of a wooden bob of mass `M` and length `l`. A bull

1.	A pendulum consists of a wooden bob of mass `M` and length `l`. A bullet of mass `m` is fired towards the pendulum with a speed `v`. The bullet emerges immediately out of the bob from the other side with a speed of `v//2` and the bob starts rising. Assume no loss of mass of bob takes place due to penetration. If the bob stops where the string becomes horizontal then `v` isA. `(2M)/m sqrt(3gl)`B. `(2M)/msqrt(5gl)`C. `(2M)/msqrt(gl)`D. `(2M)/msqrt(2gl)`
Answer» Correct Answer - D Let velocity of bob after collision be `v_(1)`. Then `Mv_(1)=(mv)/2impliesv_(1)(mv)/(2M)` Height rasised by bob `=l ` `l=v_(1)^(2)/(2g)impliesl=(m^(2)v^(2))/(8M^(2)g)impliesv=(2M)/msqrt(2gl)`

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