Question:
The energy supplied to Kolkata by the state electricity board during an average November week day was 40 GWh. If this energy could be obtained by the conservation of matter, how much mass would have to be annihilated?
The energy supplied to Kolkata by the state electricity board during an average November week day was 40 GWh. If this energy could be obtained by the conservation of matter, how much mass would have to be annihilated?
Show Hint
1 g of mass annihilated gives \(9 \times 10^{13}\) J of energy.
Updated On: Apr 23, 2026
- 1.6 g
- 2.2 g
- 4.0 g
- 1.6 kg
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept:
Einstein's mass-energy equivalence: \(E = mc^2\). \(E = 40\) GWh = \(40 \times 10^9 \times 3600\) J = \(1.44 \times 10^{14}\) J.
Step 2: Detailed Explanation:
\(m = \frac{E}{c^2} = \frac{1.44 \times 10^{14}}{(3 \times 10^8)^2} = \frac{1.44 \times 10^{14}}{9 \times 10^{16}} = 1.6 \times 10^{-3}\) kg = 1.6 g.
Step 3: Final Answer:
Thus, mass annihilated = 1.6 g.
Einstein's mass-energy equivalence: \(E = mc^2\). \(E = 40\) GWh = \(40 \times 10^9 \times 3600\) J = \(1.44 \times 10^{14}\) J.
Step 2: Detailed Explanation:
\(m = \frac{E}{c^2} = \frac{1.44 \times 10^{14}}{(3 \times 10^8)^2} = \frac{1.44 \times 10^{14}}{9 \times 10^{16}} = 1.6 \times 10^{-3}\) kg = 1.6 g.
Step 3: Final Answer:
Thus, mass annihilated = 1.6 g.
Was this answer helpful?
0
0
Top MET Physics Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- A rope of mass $0.1\, kg$ is connected at the same height of two opposite walls. It is allowed to hang under its own weight. At [he contact point between the rope and the wall, the rope makes an angle $ \theta =10^{\circ} $ with respect to horizontal. The tension in the rope at its midpoint between the walls is
- At great distances from an electric dipole, the electric field strength due to the dipole varies with the distance as
View More Questions
Top MET Electric charges and fields Questions
- Work done to rotate a dipole from \( \theta_{1} = 0^\circ \) to \( \theta_{2} = 60^\circ \) is \( W \). The work required to rotate it to \( 180^\circ \) is:
- The electric potential at a point on the axial line of an electric dipole is:
- A compound of 'A' and 'B' crystallises in a cubic lattice in which 'A' atoms occupy the lattice points at the corners of the cube. The 'B' atoms occupy the centre of each face of the cube. The probable empirical formula of the compound is
- The characteristic not related to alkali metal is
- An electric dipole shown in the figure. Work done to move a charge particle of \(1\mu C\) from point Q to P is \(x \times 10^{-7} J\), then the value of \(x\) is:
View More Questions
Top MET Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- $\int\limits_{0}^{8}| x -5| d x$ is equal to
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- Which of the following product is formed in the reaction $ CH_3MgBr {->[(i)CO_2][(ii)H_2O]} ? $
View More Questions