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:

$A$ particle of mass $25 \, g$ has an uncertainty in position of $10^{-5} \, m$. The uncertainty in velocity is ... (Planck's constant $h = 6.6 \times 10^{-34} \, J \cdot s$).

Based on Heisenberg's uncertainty principle,the uncertainty in the velocity of the electron to be found within an atomic nucleus of diameter $10^{-15} \ m$ is ............. $\times 10^9 \ ms^{-1}$ (nearest integer)
[Given : mass of electron $= 9.1 \times 10^{-31} \ kg$,Plank's constant $(h) = 6.626 \times 10^{-34} \ Js$ ]
(Value of $\pi = 3.14$ )

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 a proton is accelerated to a velocity of $3 \times 10^7 \text{ ms}^{-1}$ which is accurate up to $\pm 0.5 \%$,then the uncertainty in its position will be $\ldots \ldots \ldots$ [mass of proton $= 1.66 \times 10^{-27} \text{ kg}$,$h = 6.6 \times 10^{-34} \text{ Js}$]