Question

# A bullet of 5 g is fired from a pistol of 1.5 kg. If the recoil velocity of pistol is 1.5 ms, find the velocity of bullet. (in ms) 450 ms 500 ms 600 ms 400 ms

Solution

## The correct option is A 450 ms Here, we have, Mass of bullet, m1=5 g =51000 kg =0.005 kg Mass of pistol, m2=1.5 kg Recoil velocity of pistol $$v_2 = 1.5$$ m/s We have to find the velocity of the bullet, v1. Since, before firing, the bullet and pistol are in rest, thus Initial velocity of bullet, u1=0 And initial recoil velocity of pistol, u2=0 We know that, $$m_1 u_1+m_2 ​​u_2​​​​​​​ = m_1 v_1​​​​​​​+m_2 v_2$$​​​​​​​ ⇒0.005×0+1.5×0=0.005×v1+1.5×1.5 ms) ⇒0=0.005×v1+2.25 kgms ⇒0.005×v1=−2.25 kgms ⇒v1=−2.250.005=−450 ms Thus, the velocity of bullet =450 ms, here negative sign shows that, bullet moves in the opposite direction of recoiling of the gun.

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