Abullet of mass m and speed v passes completely through a pendulum bob of mass m. the bullet emerges with a speed of v/2. the pendulum bob is suspended by a stiff rod of length l and negligible mass. use conservation of energy and momentum to find the minimum value of v such that the bob will barely swing through a complete vertical circle.

Explanation:

After bullet passing through the pendulum we know that the pendulum will raise to its maximum height

So the minimum speed required for this is in such a way that it will reach at highest point with zero speed

so here we can use energy conservation

so we will have

now we got the speed of the pendulum so we can use now momentum conservation of bullet + pendulum system

here we have

so we have

so the speed is given as

the working equation for the angular size is the product of the physical size and 360 degrees divided by the product of two pi and distance from earth. the minimum size would be 0.559 degrees while the maximum size would be 0.49 degrees. 

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