Question

If M denotes angular momentum and p denotes linear momentum, the dimensions of \(\frac{M}{p}\) is-
1. [L²]
2. [L⁰]
3. [L¹]
4. [L³]

Answer 1

Correct Answer - Option 3 : [L¹]

The correct answer is option 3) i.e. [L1]

CONCEPT:

• The dimensional formula is used to express any physical quantity in terms of fundamental quantities.
  • Fundamental quantity: A quantity that can be measured is called a physical quantity. Fundamental quantities are those which cannot be expressed or measured in terms of other physical quantities. 
  • The seven fundamental quantities along with their dimensions are as follows:

Fundamental quantity	Dimension
Time	T
Mass	M
Electric current	A
Thermodynamic temperature	K
Amount of substance	mol
Luminous intensity	cd
Length	L

EXPLANATION:

• Linear momentum is the measure of impact caused due to a moving object with mass. It is given by the formula

Linear momentum, p = mv

Where m is the mass and v is the velocity.

• Angular momentum (M) is the rotational equivalent of linear momentum.

It is given by the formula:

Angular momentum, M = r × mv

Where m is the mass, r is the radius and v is the velocity.

Ratio = \(\frac{M}{p} = \frac{rmv}{mv} = r\)

• The dimension of r is [L¹]
• Thus, the dimensions of \(\frac{M}{p}\) is [L1]