To determine the physical quantity represented by the dimension
[ML−1T−2], let's analyze the dimensions of each of the given options step-by-step:
Option A: Pressure
× Area
Pressure has the dimension
[ML−1T−2] and Area has the dimension
[L2].
Thus:
[ML−1T−2]×[L2]=[ML‌T−2]This does not match
[ML−1T−2].
Option B:
‌| ‌ Force ‌ |
| ‌ Pressure ‌ |
Force has the dimension
[MLT−2] and Pressure has the dimension
[ML−1T−2].
Thus:
‌=[L2]This does not match
[ML−1T−2].
Option C: Power
× Time
Power has the dimension
[ML2T−3] and Time has the dimension
[T].
Thus:
[ML2T−3]×[T]=[ML2T−2]This does not match
[ML−1T−2].
Option D: Energy density
Energy density has the dimension [ Energy Volume
].
Energy has the dimension
[ML2T−2] and Volume has the dimension
[L3].
Thus:
‌=[ML−1T−2]This matches
[ML−1T−2].
Hence, the correct answer is:
Option D: Energy density