Question

The energy released in a modest size atomic bomb (20 kiloton) is about ${10}^{14}$ J. On a monsoon day in Mumbai, there was a heavy rainfall of about 100 cm over an area of about 100 $k{m}^2$. The energy released in the atmosphere on that day is roughly equivalent to that released in:

(Assume average height of clouds to be 2000 m)

• A. 20 atomic bombs
• B. 100 atomic bombs
• C. Atomic bomb
• D. Negligible compared to an atomic bomb

Answer 1

Answer: (A)

20 atomic bombs

Change in potential energy of water:

$\Delta E=mgh$ where $h:$ height of clouds

$=\rho Vgh$

$=\rho A{h}^{\prime }gh$ where $h^{\prime }:$ rainfall depth

$={10}^3\times 100\times {10}^6\times 1\times 10\times 2\times {10}^3$

$=2\times {10}^{15}J$

One atom bomb releases ${10}^{14}J$ of energy.

Hence, energy released is equivalent of $\frac{2\times {10}^{15}}{{10}^{14}}=20$ atom bombs.