The energy E and momentum p of a moving body of mass m are related by some equation. Given that c represents the speed of light, identify the correct equation. [2025]

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Q.
The energy E and momentum p of a moving body of mass m are related by some equation. Given that c represents the speed of light, identify the correct equation. [2025]

1 $E^{2} = p c^{2} + m^{2} c^{4}$

2 $E^{2} = p c^{2} + m^{2} c^{2}$

3 $E^{2} = p^{2} c^{2} + m^{2} c^{2}$

4 $E^{2} = p^{2} c^{2} + m^{2} c^{4}$

Ans.
(4)

We need to check the dimensions only.

$[E] = M^{1} L^{2} T^{- 2}$

$[P c] = M^{1} L^{1} T^{- 1} \cdot L^{1} T^{- 1} = M^{1} L^{2} T^{- 2}$

$[m c^{2}] = M^{1} L^{2} T^{- 2}$

So, $E^{2} = p^{2} c^{2} + m^{2} c^{4}$ (dimensionally)

Solution

Q.
The energy E and momentum p of a moving body of mass m are related by some equation. Given that c represents the speed of light, identify the correct equation. [2025]

1 $E^{2} = p c^{2} + m^{2} c^{4}$

2 $E^{2} = p c^{2} + m^{2} c^{2}$

3 $E^{2} = p^{2} c^{2} + m^{2} c^{2}$

4 $E^{2} = p^{2} c^{2} + m^{2} c^{4}$

Ans.
(4)

We need to check the dimensions only.

$[E] = M^{1} L^{2} T^{- 2}$

$[P c] = M^{1} L^{1} T^{- 1} \cdot L^{1} T^{- 1} = M^{1} L^{2} T^{- 2}$

$[m c^{2}] = M^{1} L^{2} T^{- 2}$

So, $E^{2} = p^{2} c^{2} + m^{2} c^{4}$ (dimensionally)

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Solution

Q. The energy E and momentum p of a moving body of mass m are related by some equation. Given that c represents the speed of light, identify the correct equation. [2025]

1 E2=pc2+m2c4

2 E2=pc2+m2c2

3 E2=p2c2+m2c2

4 E2=p2c2+m2c4

Ans. (4) We need to check the dimensions only. [E]=M1L2T–2 [Pc]=M1L1T–1·L1T–1=M1L2T–2 [mc2]=M1L2T–2 So, E2=p2c2+m2c4 (dimensionally)

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Q.
The energy E and momentum p of a moving body of mass m are related by some equation. Given that c represents the speed of light, identify the correct equation. [2025]

1 $E^{2} = p c^{2} + m^{2} c^{4}$

2 $E^{2} = p c^{2} + m^{2} c^{2}$

3 $E^{2} = p^{2} c^{2} + m^{2} c^{2}$

4 $E^{2} = p^{2} c^{2} + m^{2} c^{4}$

Ans.
(4)

We need to check the dimensions only.

$[E] = M^{1} L^{2} T^{- 2}$

$[P c] = M^{1} L^{1} T^{- 1} \cdot L^{1} T^{- 1} = M^{1} L^{2} T^{- 2}$

$[m c^{2}] = M^{1} L^{2} T^{- 2}$

So, $E^{2} = p^{2} c^{2} + m^{2} c^{4}$ (dimensionally)