A 20 g bullet pierces through a plate of mass M1 = 1 kg and then comes to rest inside a second plate of mass M2 = 2.98 kg (refer figure). It is found that the two plates, initially at rest, now move with equal velocity v. Find the velocity of the bullet (in m/s) when it is between M1 and M2. Given that it entered M1 with 100 m/s.
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From the principle of conservation of linear momentum we have
mu = M1v + mv’
and mv’ = (m + M2)v
or 20u = 1000v + 20v’
and 20v’ = (20 + 2980)v
or u = 50v + v’ ...(i)
and v’ = 150 v ...(ii)
From (i) and (ii), we get 3u = v’ + 3v’ = 4v’ or v’ = 3u/4 = 75
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