A bullet of mass 10g and speed 500ms^(-1) is fired into a door and gets embedded exactly at the centre of the door. The door is 1.0m wide and weighs 12kg. It is hinged at one end and rotates about a vertical axis practically without friction. Find the angular speed of the door just after the bullet embeds into it

A bullet of mass 10g and speed 500ms^(-1) is fired into a door and get

1.	A bullet of mass 10g and speed 500ms^(-1) is fired into a door and gets embedded exactly at the centre of the door. The door is 1.0m wide and weighs 12kg. It is hinged at one end and rotates about a vertical axis practically without friction. Find the angular speed of the door just after the bullet embeds into it
Answer» Solution : M.I of door about an axis at ONE end`=(ML^2)/(3)` Given `m_b=10^(-2)KG""v_b=500ms^(-1)` `md_d=12kg,L=1m` `:.I=(12xx1^2)/3=4kgm^2` `K.E_b=1/2xxm_bv_b^2=1/2xx10^(-2)xx(500)^2=1250J` but K.E`=1/2Iomega^2`i.e `omega^2=(2K.E)/I=(2xx1250)/4` `omega^2=625` or `omega=25rads^(-1)`