Q.4: a) A pendulum of length L with a bob ofmass m is pulled aside until the bob

Question

Q.4:

a)     A pendulum of length L with a bob ofmass m is pulled aside until the bob is at a height L/4 above itsequilibrium position. The bob is then released. Find the speed ofthe bob as it passes the equilibrium position.

                            

b)     If two objects collide and one isinitially at rest, is it still possible for both to be at restafter the collision? (Any external forces acting on the two–objects system are negligibly small.) Is it possible for oneto be at rest? Explain

c)      A shell of mass m and speed vexplodes into two identical fragments. If the shell was movinghorizontally with respect to the earth, and one of thefragments is subsequently moving with speed v, find the velocityv¢ of the otherfragment       

Explanation / Answer

given inital height of the bob is h = L /4 let the mass of the bob is m then the potential energy is = mgh at the mean position it will have only the kineticenergy     let the velocity is v   thenwe have                        mgh = 1/2 mv2                    v = (2gh ) substituting the value of h we get                       v = ( gL /2 )                    v = (2gh ) substituting the value of h we get                       v = ( gL /2 )

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