JEE MAIN - Physics (2021 - 27th August Evening Shift - No. 12)
If force (F), length (L) and time (T) are taken as the fundamental quantities. Then what will be the dimension of density :
[FL$$-$$4T2]
[FL$$-$$3T2]
[FL$$-$$5T2]
[FL$$-$$3T3]
Explanation
Density = [FaLbTc]
[ML$$-$$3] = [MaLa+bT$$-$$2aLbTc]
[M1L$$-$$3] = [MaLa+bT$$-$$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 = [F1L$$-$$4T2]
[ML$$-$$3] = [MaLa+bT$$-$$2aLbTc]
[M1L$$-$$3] = [MaLa+bT$$-$$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 = [F1L$$-$$4T2]
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