Question 159: Units , Dimensions and Error Analysis

Question

If force (F), length (L) and time (T) are taken as the fundamental quantities. Then what will be the dimension of density :

Accepted Answer

Density = [F
a
L
b
T
c
]
[ML
$-$3
] = [M
a
L
a+b
T
$-$2a
L
b
T
c
]
[M
1
L
$-$3
] = [M
a
L
a+b
T
$-$2a+c
]
$\matrix{
   {a = 1} & ; & {a + b =  - 3} & ; & { - 2a + c = 0}  \cr 
   {} & {} & {1 + b =  - 3} & {} & {c = 2a}  \cr 
   {} & {} & {b =  - 4} & {} & {c = 2}  \cr

} $
So, density = [F
1
L
$-$4
T
2
]

Answer

[FL
$-$4
T
2
]

Answer

[FL
$-$3
T
2
]

Answer

[FL
$-$5
T
2
]

Answer

[FL
$-$3
T
3
]

Units , Dimensions and Error Analysis

If force (F), length (L) and time (T) are taken as the fundamental quantities. Then what will be the dimension of density :

Choose the correct answer: