Physics Questions and Answers

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In general, the energy released during nuclear fission is given by the Einstein's mass-energy equation, given by

$E = \Delta MC^2$

Where $\Delta m$ is the mass defect, and C is the speed of light.
Therefore
$\Delta m = 0.01% \text{of} 1.0g = \frac{0.01}{100} \times 1.0g \\ = 1.0 \times 10^{-4} \\ = 1.0 \times 10^{-7}kg\\ \text{Energy Released } = \Delta MC^2 \\ = 1.0 \times 10^{-7} \times (3.0 \times 10^8)^2\\ = 1.0 \times 10^{-2} \times 9.0 \times 10^{16} \\ = 9.0 \times 10^9 J$

From the uncertainty principle the product of the position and momentum of a sub-atomic particle is equal or greater than planck's constant.

i.e $\Delta x. \Delta p \geq h. \\ \text{Thus} 5 \times 10^{-10} \times \Delta p = 6.6 \times 10^{-34} \\ \Delta p = \frac{6.6 \times 10^{-34}}{5 \times 10^{-10}} = 1.32 \times 10^{-24}Ns\\ \text{Therefore Uncertainty in the momentum } = 1.32 \times 10^{-24}Ns$

The speed of sound in a material is given as:

$V = \sqrt{\frac{E}{P}}, Where\\ E = \text{Young's modulus} \\ P = \text{Density }\\ \text{Therefore } V = \sqrt{\frac{7.0 \times 10^{10}}{2.7 \times 10^3}} = 5091.75\\ = 5.1 \times 10^3MS^{-1}$

From Newton's second law:

$F = \frac{mV - mµ}{t}$

Let the final velocity = V; and since the football is initially at rest, its initial vel µ = 0, M = 0.8kg

$t = 0.8s \\ \implies 100 = \frac{0.8V - 0.8 \times 0}{0.8} \\ \text{Therefore } V = \frac{100 \times 0.8}{0.8} = 100ms^{-1}$