Question

1. The dimensional formulae of a physical quantity is [MLT^-2]. The SI unit of this physical quantity is times its CGS unit. (a) 105 (b) 107 (c)10 (d) 100​

Answer 1

Given,

Dimensional formula = [MLT⁻²]

To find,

By how many times the SI unit of the given physical quantity, is bigger than the CGS unit of that same physical quantity?

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

First of all, we have to determine the SI and CGS units.

In SI unit system,

Unit of Mass (M) = Kilogram

Unit of Length (L) = Metre

Unit of Time (T) = Second

In CGS system,

Unit of Mass (M) = Gram

Unit of Length (L) = Centimetre

Unit of Time (T) = Second

So,

Unit in SI for [MLT⁻²] = Kg.m.s⁻² = Kg.m/s²

Unit in CGS for [MLT⁻²] = g.cm.s⁻² = g.cm/s²

Now,

1 Kg.m/s² = (1×1000)g.m/s² = 1000g.m/s² = (1000×100) g.cm/s² = 100000g.cm/s²

[As, 1 kg = 1000g and 1m = 100cm]

Hence, the SI unit is 100000 times than the CGS unit.

Answer 2

Since, this is an MCQ, I will tell you a fast method that will help you in Competitive Exams a lot.

• First of all, the physical quantity has dimensions of $MLT^{-2}$.

• This means that the physical quantity is actually : Mass × Length/Time² = Mass × Acceleration = Force.

So, SI UNIT of FORCE is Newton (N) and CGS UNIT of FORCE is dyne.

Now, we know , 1 N = 10⁵ dyne (remember this)

So, SI UNIT = 10⁵ times CGS unit.