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: $h = 6.6 \times 10^{-34} \ J \ s$)

What will be the mass of a particle if uncertainty in its position is $10^{-8} \ m$ and uncertainty in velocity is $5.26 \times 10^{-25} \ m \ s^{-1}$? ............... $kg$

The uncertainties in the velocities of particles $A$ and $B$ are $0.05 \, m/s$ and $0.02 \, m/s$,respectively. If the mass of particle $B$ is five times that of particle $A$,then the ratio of the uncertainties in their positions $\left( \frac{\Delta x_A}{\Delta x_B} \right)$ is equal to:

Given below are two statements $:$
Statement $(I):$ It is impossible to specify simultaneously with arbitrary precision,both the linear momentum and the position of a particle.
Statement $(II) :$ If the uncertainty in the measurement of position and uncertainty in measurement of momentum are equal for an electron,then the uncertainty in the measurement of velocity is $\geq \sqrt{\frac{h}{4\pi}} \times \frac{1}{m}$ which simplifies to $\geq \frac{1}{2m} \sqrt{\frac{h}{\pi}}$. In the light of the above statements,choose the correct answer from the options given below $:$

The uncertainties in the velocities of two particles,$A$ and $B$ are $0.05 \ ms^{-1}$ and $0.02 \ ms^{-1}$ respectively. The mass of $B$ is five times that of the mass of $A$. What is the ratio of uncertainties $\frac{\Delta x_A}{\Delta x_B}$ in their positions?

If the uncertainty in momentum of a particle is twice the uncertainty in its position,what will be the uncertainty in the position of the particle?