A golf ball of mass m has a speed of 50 m s | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The uncertainty in the speed $\Delta v$ is $2 \%$ of $50 \ m \ s^{-1}$.$\Delta v = 50 	imes \frac{2}{100} = 1 \ m \ s^{-1}$.According to Heisenbe

Vedclass · Accepted Answer

$\frac{h}{4 \pi m}$

Vedclass · Answer

(A) The uncertainty in the speed $\Delta v$ is $2 \%$ of $50 \ m \ s^{-1}$.$\Delta v = 50 	imes \frac{2}{100} = 1 \ m \ s^{-1}$.According to Heisenberg's uncertainty principle,$\Delta x \cdot \Delta p \geq \frac{h}{4 \pi}$.Since $\Delta p = m \Delta v$,we have $\Delta x = \frac{h}{4 \pi m \Delta v}$.Substituting the value of $\Delta v = 1 \ m \ s^{-1}$:$\Delta x = \frac{h}{4 \pi m 	imes 1} = \frac{h}{4 \pi m}$.Wait,re-evaluating the calculation: The question implies the uncertainty in speed is $1 \ m \ s^{-1}$.$\Delta x = \frac{h}{4 \pi m (1)} = \frac{h}{4 \pi m}$.However,looking at the provided options,if the mass $m$ is in $kg$ and we consider standard units,the calculation leads to $\frac{h}{4 \pi m}$.Given the options,if the result is $\frac{h}{4 \pi m}$,option $A$ is correct.

$A$ golf ball of mass $m$ has a speed of $50 \ m \ s^{-1}$. If the speed can be measured within an accuracy of $2 \%$,the uncertainty in the position is

Similar Questions

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?

The Bohr model of an atom is contradicted by

Which of the following statements is $correct$?

The uncertainty in the position of a particle of mass $0.25 \, kg$ is $10^{-5} \, m$. The uncertainty in its velocity is ...... $m/s$.

Why was a change in the Bohr Model of atom required? Due to which important development$(s)$,was the concept of movement of an electron in an orbit replaced by the concept of probability of finding an electron in an orbital? What is the name given to the changed model of atom?

Vedclass Test Series

Exam Paper Generator

Online Exam Module