The square root of the dimension of energy divided by mass is the same as that of:
- Aacceleration
- Btime
- Cvelocity
- Ddisplacement
Solution & Step-by-step Explanation
Let's analyze the dimensions of the given physical quantities:
The dimensional formula for Energy (E) is:
[E]=[ML
2
T
−2
]
The dimensional formula for Mass (m) is:
[m]=[M]
Now, divide the dimension of energy by mass:
[m]
[E]
=
[M]
[ML
2
T
−2
]
=[L
2
T
−2
]
Taking the square root of this value:
[m]
[E]
=
[L
2
T
−2
]
=[LT
−1
]
The dimension [LT
−1
] represents velocity.
The dimensional formula for Energy (E) is:
[E]=[ML
2
T
−2
]
The dimensional formula for Mass (m) is:
[m]=[M]
Now, divide the dimension of energy by mass:
[m]
[E]
=
[M]
[ML
2
T
−2
]
=[L
2
T
−2
]
Taking the square root of this value:
[m]
[E]
=
[L
2
T
−2
]
=[LT
−1
]
The dimension [LT
−1
] represents velocity.