Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

Concepts Of Physics MCQ Edition [Volume 2]

Exam: Concepts Of Physics MCQ Edition [Volume 2]
Subject: Physics
Chapter: Electric Field and Potential

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Electric Field and Potential

Consider an attractive nuclear force acting between two protons...

Consider an attractive nuclear force acting between two protons that can be expressed as

F = Ce^{-kr}/r^2

. Determine the dimensional formulae and appropriate SI units of

C

and

k

.

Options

A $[M L^3 T^{-2}]$ , $[L]$ , $\text{N m}^2$ , $\text{m}$
B $[M L^3 T^{-2}]$ , $[L^{-1}]$ , $\text{N m}^2$ , $\textm^{-1}$
C $[M L T^{-2}]$ , $[L^{-1}]$ , $\text{N}$ , $\textm^{-1}$
D $[M L^2 T^{-2}]$ , $[L^{-2}]$ , $\text{J}$ , $\textm^{-2}$

Correct answer

B. $[M L^3 T^{-2}]$ , $[L^{-1}]$ , $\text{N m}^2$ , $\textm^{-1}$

Step-by-step solution

The given equation is

F = \dfrac{C e^{-kr}}{r^2}

.

Since the exponent of an exponential function must be dimensionless, the term

kr

is dimensionless.

[k][r] = [M^0 L^0 T^0]

[k] = \dfrac{1}{[r]} = [L^{-1}]

The SI unit of

k

is

\textm^{-1}

.

The exponential term

e^{-kr}

is dimensionless, so the dimensions of

F

and

\dfrac{C}{r^2}

must be the same.

[F] = \dfrac{[C]}{[r^2]}

[C] = [F][r^2] = [M L T^{-2}][L^2] = [M L^3 T^{-2}]

The SI unit of

C

is

\text{N m}^2

.

Practice Electric Field and Potential on Quantrex Academy →

More from Electric Field and Potential

Determine the dimensional formula of ε_0 . Concepts Of Physics MCQ Edition [Volume 2]Two equal charges are situated at a separation of 1.0 m . What must be the magnitude of… Concepts Of Physics MCQ Edition [Volume 2]Determine the electric force between two protons separated by a distance of 1 fermi ( 1… Concepts Of Physics MCQ Edition [Volume 2]Two charges of 2.0 × 10^ -6 C and 1.0 × 10^ -6 C are located at a separation of 10 cm .… Concepts Of Physics MCQ Edition [Volume 2]A 1.0 C charge is positioned at the top of a college building, while another equal charge… Concepts Of Physics MCQ Edition [Volume 2]Determine the separation at which two equal charges of 1.0 C each must be placed so that… Concepts Of Physics MCQ Edition [Volume 2]Two charges of 2.0 × 10^ -6 C and -1.0 × 10^ -6 C are placed at a separation of 10 cm .… Concepts Of Physics MCQ Edition [Volume 2]Two charged particles are separated by a distance of 1.0 cm . Determine the minimum… Concepts Of Physics MCQ Edition [Volume 2] Full Electric Field and Potential list All Concepts Of Physics MCQ Edition [Volume 2] PYQs