Question

One gram of mass is equal to:
(A) $ 5\times {{10}^{10}} $ erg
(B) $ 9\times {{10}^{20}} $ erg
(C) $ 7\times {{10}^{5}} $ erg
(D) $ 11\times {{10}^{12}} $ erg

Answer 1

Hint: To find out the amount of mass in terms of energy we need to use Einstein’s Mass-Energy equivalence relationship which is based upon the special theory of relativity by Einstein.

Formula: $ \text{E = m }{{\text{c}}^{\text{2}}} $
Where E is the energy of the body, m is the mass of the body, and c is the speed of light.

Complete Step by Step Answer
The special theory of relativity or the special relativity is theory which is based on the relationship between space and time. This theory of relativity is mainly based on two laws:
-The laws of physics are invariant in all inertial frames of reference (i.e. those frames which have no acceleration).
-The speed of light in vacuum is the same for all observers, regardless of the motion of the light source or the observer.
Combined with the other laws of physics, the two postulates of the special theory of relativity predict the equivalence of mass and energy. It states that when the speed of any physical entity becomes equal to the speed of light then the mass of the body is converted to energy.
Mathematically,
 $ \text{E = m }{{\text{c}}^{\text{2}}} $
Where E is the energy of the body, m is the mass of the body, and c is the speed of light.
Putting the mass of the body = 1 g in the above equation we get,
 $ \text{E =1}\times {{\left( 3\times {{10}^{10}} \right)}^{\text{2}}}=9\times {{10}^{20}} $ (the speed of light in vacuum = $ 3\times {{10}^{10}} $ $ \text{cm/ sec} $ )
Therefore the correct answer is option B.

Note
The special theory of relativity has a number of consequences that have even been experimentally verified, these include the length correction, time dilation, the relativistic velocity addition formula, relativistic mass, etc. to name some.