Question

A neutron of mass $1.67\times {10}^{-27}kg$ is moving with a velocity $1.2\times {10}^{7}m{s}^{-1}$ collides head-on with a deuteron of mass $3.34\times {10}^{-27}kg$ initially at rest. If the collision is perfectly inelastic, the speed of the composite particle will be

• A. $2\times {10}^{6}m{s}^{-1}$
• B. $4\times {10}^{6}m{s}^{-1}$
• C. $6\times {10}^{6}m{s}^{-1}$
• D. $8\times {10}^{6}m{s}^{-1}$

Answer 1

The correct option is B $4\times {10}^{6}m{s}^{-1}$

Mass of neutron (m) = $1.67\times {10}^{-27}$ kg. Speed of neutron (v) = $1.2\times {10}^{7}m{s}^{-1}$. Notice that the mass of deuteron (M) = $3.34\times {10}^{-27}kg=2m$. If V is the speed of the composite particle, the law of conservaton of momentum gives mv = (m+M)V
or $V=\frac{mv}{m+M}=\frac{mv}{m+2m}$
or $V=\frac{v}{3}=\frac{1.2\times {10}^7}{3}=4\times {10}^{6}m{s}^{-1}$, which is choice (b).