Question

(a) A body of mass m is moving with a velocity
Write the expression for its kinetic energy.
(b) Show that the quantity 2K/v2 has the unit of
mass, where K is the kinetic energy of the body.​

Answer 1

Answer:

Question 1 )

Mass m ia moving with velocity v .

Hence the body possess some amount of energy by the virtue of it's motion. That energy is called Kinetic energy.

$\boxed{ \red{ \huge{ \bold{KE = \frac{1}{2} m {v}^{2} }}}}$

Question 2 )

A quantity has been given as follows :

$\boxed{\dfrac{2K}{ {v}^{2} }} \: \sf{ is \: the \: quantity}$

Let's rearrange the equation from the 1st question , we can say that :

$\blue{ \huge{ \bold{KE = \frac{1}{2} m {v}^{2} }}}$

$\blue{ \bold{ \huge{ = > m = \frac{2KE}{ {v}^{2} } }}}$

So it's proved that the given Quantity has equivalent Dimensions as that of mass.

Additional information on Dimensions :

• Only quantities of same Dimensions can be added.
• Dimensions are useful for assessing the validity of any equation.

Answer 2

$\huge \underline {\underline{ \mathfrak{ \green{Ans}wer \colon}}}$

(a) A body of mass m is moving with a velocity

Write the expression for its kinetic energy.

We have expression for Kinetic Energy :

$\large{\boxed{\boxed{\sf{K.E \: = \: \dfrac{1}{2} mv^2}}}}$

Where,

• m is mass
• v is velocity
• K.E is kinetic energy

✯ Kinetic energy comes to play when object is in state of motion.

✯ SI Unit of Energy is Joule (J) .

_______________________________

(b) Show that the quantity 2K/v2 has the unit of mass, where K is the kinetic energy of the body.

As we know that :

$\large \implies {\sf{K.E \: = \: \dfrac{1}{2} mv^2}} \\ \\ \large \implies {\boxed{\sf{m \: = \: \dfrac{2K}{v^2}}}}$

• So, the the quality 2K/v² is a unit mass.

✯ Mass is a fundamental quantity.

✯ Mass is denoted by m.

✯ S.I unit is Kg.

✯ Mass is a scaler quantity.