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 $:$

  • A
    Statement $I$ is true but Statement $II$ is false.
  • B
    Both Statement $I$ and Statement $II$ are true.
  • C
    Statement $I$ is false but Statement $II$ is true.
  • D
    Both Statement $I$ and Statement $II$ are false.

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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:

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The uncertainty in the position of an electron $(mass = 9.1 \times 10^{-28} \ g)$ moving with a velocity of $3.0 \times 10^4 \ cm \ s^{-1}$ accurate up to $0.001\%$ will be ................. $cm$ (Use $\frac{h}{4\pi}$ in the uncertainty expression,where $h = 6.626 \times 10^{-27} \ erg \ s$)

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