Question
A pulse of light of duration $$100\,ns$$ is absorbed completely by a small object initially at rest. Power of the pulse is $$30\,mW$$ and the speed of light is $$3 \times {10^8}m{s^{ - 1}}.$$ The final momentum of the object is
A.
$$0.3 \times {10^{ - 17}}kg\,m{s^{ - 1}}$$
B.
$$1.0 \times {10^{ - 17}}kg\,m{s^{ - 1}}$$
C.
$$3.0 \times {10^{ - 17}}kg\,m{s^{ - 1}}$$
D.
$$9.0 \times {10^{ - 17}}kg\,m{s^{ - 1}}$$
Answer :
$$1.0 \times {10^{ - 17}}kg\,m{s^{ - 1}}$$
Solution :
$$p = \frac{E}{c} = \frac{{P \times t}}{c} = \frac{{30 \times {{10}^{ - 3}} \times 100 \times {{10}^{ - 9}}}}{{3 \times {{10}^8}}} = {10^{ - 17}}kg\,m{s^{ - 1}}$$
option (B) is correct