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Question

Answers

A. L

B. L

C. L

D. MLT

Answer
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Linear momentum of an object is given by the formula:

$p = mv$

Where,

p is the linear momentum of the object

m is the mass of the object

v is the velocity of the object

Angular momentum, (also known as moment of momentum) is mathematically the product of moment of inertia and angular velocity. It is also known as the inertia of rotational motion.

Angular momentum of an object is given by the formula:

$L = r \times mv$

Where,

L is the angular momentum of the object

r is the distance of point of application of Force from its centre of mass

Linear momentum of an object is given by the formula:

$p = mv$ ……….Equation 1

Where,

p is the linear momentum of the object

m is the mass of the object

v is the velocity of the object

Angular momentum of an object is given by the formula:

$L = r \times mv$ …………..Equation 2

Where,

L is the angular momentum of the object

r is the distance of point of application of Force from its centre of mass

Now, we are required to compute the ratio of angular momentum to linear momentum.

Dividing Equation 2 by Equation 1,

We get,

$ = > \dfrac{L}{p} = \dfrac{{r \times mv}}{{mv}}$

$ = > \dfrac{L}{p} = r$

We know that the dimensional formula of r is [L1]

Hence dimensional formula of $\dfrac{L}{p}$ is,

\[ = > \dfrac{L}{p} = [{L^1}]\]