Question

A body of mass m moving with a speed v suffers an inelastic collision with another body of M at rest and sticks to it. The speed of the composite body will be

• A. $\left(\frac{m+M}{m}\right)v$
• B. $\left(\frac{m}{m+M}\right)v$
• C. $\left(\frac{M}{m+M}\right)v$
• D. $\left(\frac{m+M}{M}\right)v$

Answer 1

The correct option is B $\left(\frac{m}{m+M}\right)v$

Initial momentum of the system = mv, since body of mass M is at rest. After the inelastic collision, the bodies stick together and the mass of the composite body is (m + M). If V is the speed of the composite
body, its momentum will be (m + M)V. From the principle of conservation of momentum, we have mv = (m + M)V
or $V=\left(\frac{m}{m+M}\right)v$
Hence the correct choice is (b).