Question

The energy supplied to Kolkata by the state electricity board during an average November week day was 40 gigawatt hour. If the energy could be obtained by the conservation of matter, how much mass would have to be annihilated ?
a. 1.6 gm
b. 2.2 gm
c. 4.0 gm
d. 1.6 kg

Answer 1

Hints: According to the mass energy relation of Einstein $\left[ {E = m{c^2}} \right]$ every mass can be converted into energy when it travels with the speed of light. By using the energy mass equation we can easily find out the required mass.

Complete step by step solution :
Given:
Velocity of light, c = $3 \times {10^8}m{s^{ - 1}}$
Energy, E = 40 gigawatt hour = $40 \times {10^9} \times 60 \times 60$watt sec
On converting the unit in S.I. units we get

$\therefore $E = $1.44 \times {10^{14}}$watt hr

Using the energy mass relation,
$E = m{c^2}$

Putting the values of E, c we get
$1.44 \times {10^{14}} = m \times {\left( {3 \times {{10}^8}} \right)^2}$

$m = \dfrac{{1.44 \times {{10}^{14}}}}{{9 \times {{10}^{16}}}}kg$

$m = 1.6 \times {10^{ - 3}}kg$

On converting the mass in gm we get,
$m = 1.6gm$

Hence the correct option is A.

Note: On putting the values of different quantities all should be in the S.I. unit in order to get the correct answer otherwise the answer may get wrong. Also take care of unit conversion in each step of solution.