91Ó°ÊÓ

The given data is listed below as-

• The mass of the meteor is $\mathrm{m}=1.4×{10}^8\mathrm{kg}$
• The speed of the meteor hitting the ground is,$\mathrm{V}=12\mathrm{km}/\mathrm{s}=12000\mathrm{m}/\mathrm{s}$
• The kinetic energy of one ton of TNT is${\mathrm{K}}_{\mathrm{TNT}}=4.184×{10}^9\mathrm{J}$

The kinetic energy of a particle equals the amount of work required to accelerate the particle from rest to speed V. Therefore, kinetic energy on the particle is given by-

$\mathbf{K}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{mV}}^{\mathbf{2}}$

The kinetic energy is a scalar and it is always positive or zero.

The amount of kinetic energy which meteor deliver to the ground will be

$\mathrm{K}=\frac{1}{2}{\mathrm{mV}}^2$

Here, m is the mass of the meteor, and V is the speed of the meteor hitting the ground.

For,$\mathrm{m}=1.4×{10}^8\mathrm{kg}$, and$\mathrm{V}=12\mathrm{km}/\mathrm{s}=12000\mathrm{m}/\mathrm{s}$

The kinetic energy will be

$$\begin{gathered} \mathrm{K}=\frac{1}{2}{\mathrm{mV}}^2 \\ =\frac{1}{2}×1.4×{10}^8\mathrm{kg}×{\left(12×{10}^3{\mathrm{ms}}^{-1}\right)}^2 \\ =100.8×{10}^{14}\mathrm{J} \\ =1.01×{10}^{16}\mathrm{J} \end{gathered}$$$$\begin{gathered} \mathrm{K}=\frac{1}{2}{\mathrm{mV}}^2 \\ =\frac{1}{2}×1.4×{10}^8\mathrm{kg}×{\left(12×{10}^3{\mathrm{ms}}^{-1}\right)}^2 \\ =100.8×{10}^{14}\mathrm{J} \\ =1.01×{10}^{16}\mathrm{J} \end{gathered}$$

Thus, the kinetic energy delivered by meteor to the ground is $1.01×{10}^{16}\mathrm{J}$.

The energy released by 1.0 ton of TNT

Therefore, energy released by one million tons of TNT

For Comparison of energy released by meteor that hits the ground to the energy released by 1.0-megaton nuclear bomb divide the meteor’s kinetic energy by the energy of the megaton bomb.

Therefore,

$$\begin{gathered} \frac{{\mathrm{K}}_{\mathrm{M}}}{{\mathrm{K}}_{\mathrm{MB}}}=\frac{1.01×{10}^{16}\mathrm{J}}{4.184×{10}^{15}\mathrm{J}} \\ \frac{{\mathrm{K}}_{\mathrm{M}}}{{\mathrm{K}}_{\mathrm{MB}}}=2.4 \end{gathered}$$

Hence,

${\mathrm{K}}_{\mathrm{M}}=2.4{\mathrm{K}}_{\mathrm{MB}}$

Thus, the energy released by a meteor is 2.4 times energy of the megaton bomb.