Question
Table-tennis ball has a mass $$10\,g$$ and a speed of $$100\,m/s.$$ If speed can be measured within an accuracy of $$10\% ,$$ what will be the uncertainty in speed and position respectively ?
A.
$$10\,m/\sec ,4 \times {10^{ - 33}}\,m$$
B.
$$10\,m/\sec ,5.27 \times {10^{ - 34}}\,m$$
C.
$$0.1\,m/\sec ,5 \times {10^{ - 34}}\,m$$
D.
$${\text{None of these}}$$
Answer :
$$10\,m/\sec ,5.27 \times {10^{ - 34}}\,m$$
Solution :
$${\text{Uncertainty in the speed of ball}}$$ $$ = \frac{{100 \times 10}}{{100}} = 10\,m/s$$
$$\Delta x.m\Delta v = \frac{h}{{4\pi }}$$
$$\eqalign{
& {\text{Uncertainty in the position,}} \cr
& \Delta x = \frac{h}{{4\pi m\Delta v}} \cr
& \,\,\,\,\,\,\,\, = \frac{{6.626 \times {{10}^{ - 34}}}}{{4 \times 3.14 \times 10 \times {{10}^{ - 3}} \times 10}} \cr
& \,\,\,\,\,\,\,\, = 5.27 \times {10^{ - 34}}\,m \cr} $$