Question

7. Which of the following have the
same dimensions as v2r Where v is
the speed of the particle describing a
circular path of radius r?
*
(a) Force (b) Impulse
(c) Acceleration
(d) Momentum​

Answer 1

HELLO DEAR,

GIVEN:-

Which of the following have the

same dimensions as v²/r . Where v is

the speed of the particle describing a circular path of radius r?

(a) Force

(b) Impulse

(c) Acceleration

(d) Momentum

ANSWER:- Lets find the dimension of v²/r, where v= velocity and r = radius.

Dimension of v²/r = [ L²/T²] /[L]

= [ M°LT⁻² ]

And the dimension of acceleration = [ M°LT⁻² ]

Therefore , correct option is (c) Acceleration.

THANKS.

Answer 2

Given:

Here 'v' is Velocity and 'r' is Radius.

To find:

Dimension of the options same to v²/r?

Calculation:

• Dimensions of Velocity will be $[LT^{-1}]$.
• Dimensions of radius is [L].

$\rm \therefore\bigg[ \dfrac{ {v}^{2} }{r} \bigg]$

$\rm = \bigg[ \dfrac{ { \bigg({M}^{0} L{T}^{ - 1} \bigg)}^{2} }{L} \bigg]$

$\rm = \bigg[ \dfrac{ {L }^{2} {T}^{ - 2} }{L} \bigg]$

$\rm = \bigg[ L {T}^{ - 2} \bigg]$

$\rm = \bigg[ acceleration \bigg]$

[v²/r] dimension is similar to that of Acceleration.