A large block of wood of mass $$M=5.99$$ kg is hanging from two long massless cords. A bullet of mass m $$=$$ $$10$$ g is fired into the block and gets embedded in it. The (block+bullet) then swing upwards, their center of mass rising a vertical distance $$h=9.8$$ cm before the (block+bullet) pendulum comes momentarily to rest at the end of its arc . The speed of the bullet just before collision is:(take$$ $$g=9.8$$ $$ms-2)

Question

A large block of wood of mass $$M=5.99$$ kg is hanging from two long massless cords. A bullet of mass m $$=$$ $$10$$ g is fired into the block and gets embedded in it. The (block+bullet) then swing upwards, their center of mass rising a vertical distance $$h=9.8$$ cm before the (block+bullet) pendulum comes momentarily to rest at the end of its arc . The speed of the bullet just before collision is:(take$$ $$g=9.8$$ $$ms-2)

Infinity Learn · Accepted Answer

Conservation of $$momentumPi=Pf$$ ⇒$$0.01$$ ×$$u+0$$   $$=6$$×v  ⇒$$v=0.01u6Using$$ energy conservation , after collision ⇒$$12$$×$$6$$×$$u6002=6$$×$$9.8$$×$$9.8$$×$$10$$−$$2$$⇒$$u=6$$×$$98$$×$$2=5882$$  $$m/s=831.4$$ $$m/s$$

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