The uncertainty in the velocities of two particles $A$ and $B$ are $0.03 \ m \ s^{-1}$ and $0.01 \ m \ s^{-1}$ respectively. The mass of $B$ is four times the mass of $A$. The ratio of uncertainties in their positions is

The position of both an electron and a helium atom is known within $1.0 \, nm$ and the momentum of the electron is known within $50 \times 10^{-26} \, kg \, m \, s^{-1}$. The minimum uncertainty in the measurement of the momentum of the helium atom is

If the uncertainty in velocity of electron $(\Delta v)$ is $0.1 \ m/s$,the uncertainty in its position $(\Delta x)$ is (given: $m_e = 9.1 \times 10^{-31} \ kg$)

The uncertainty of velocity of an electron is $5.7 \times 10^5 \ m \ s^{-1}$. Find its uncertainty in position.

The uncertainty in the determination of the position of a small ball of mass $10 \ g$ is $10^{-33} \ m$. With what percentage of accuracy can its speed be measured, if it has a speed of $52.5 \ m \ s^{-1}$? (Given: $h = 6.6 \times 10^{-34} \ J \ s$)

If uncertainties in the measurement of position and momentum of a microscopic object of mass $m$ are equal,then the uncertainty in the measurement of velocity is given by the expression: