A bullet of mass $$10gmoving$$ horizontally with a velocity of $$400$$ $$ms-1$$ strikes a wood block of mass $$2$$ kg which is suspended by light inextensible string of length $$5m$$. As a result, the centre of gravity of the block found to rise a vertical distance of $$10$$ cm. The speed of the bullet after it emerges out horizontally from the block will be

Question

A bullet of mass $$10gmoving$$ horizontally with a velocity of $$400$$ $$ms-1$$ strikes a wood block of mass $$2$$ kg which is suspended by light inextensible string of length $$5m$$. As a result, the centre of gravity of the block found to rise a vertical distance of $$10$$ cm. The speed of the bullet after it emerges out horizontally from the block will be

Infinity Learn · Accepted Answer

We can apply work energy theorem for the bullet and block before strike and after the bullet is ejected out of the blockFrom conservation of linear momentum $$101000$$×$$400$$ $$+$$ $$0$$ $$=$$ $$2v1$$ $$+$$ $$101000v2$$ From work energy theorem Wgr $$=$$ ∆K.E⇒$$2g$$×yC.$$G=12$$×$$2$$×$$v12$$  solving we get $$v1=2m/$$$$sec$$ and $$v2=120m/$$$$sec$$

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