Question

name at least two physical quantities whose dimensions are ML2T-2​

Answer 1

Answer:

Work, Kinetic energy, Potential energy......

Explanation:

Work:

force * displacement

=[MLT^-2][L] = [ML^2T^-2]

KINETIC ENERGY

=1/2*mass* $velocity^{2}$

=[M][LT^-1]^2

=[ML^2T^-2]

similarly, you can get potential energy by applying its formula

Hope it helps you.

:-)

Answer 2

Answer:

Explanation:

Definition of work:

Work is the result of the displacement's magnitude and the component of force acting in that direction.

The preceding sentence can be stated mathematically as follows:

$W = (F cos θ) d = F. d$

W stands for the force's work in this equation.

F represents the force, while d is the force-caused displacement.

The force vector's angle with the displacement vector is called.

Dimensional Formula for Work:

The dimensional formula of Work is given by,

$M L^{2} T^{-2}$

Where,

• M = Mass
• L = Length
• T = Time

Derivation:

$Work (W) = Force * Displacement . . . . . (1)$

$Since, Force = Mass * acceleration = M * [L T^{-2} ]$

∴ The dimensional formula of Force $=$$M^{1} L ^{1} T ^{-2} . . . . (2)$

On substituting equation (2) in equation (1) we get,

$Work = Force * Displacement$

$Or, W = [M^{1} L^{1} T^{-2} ] * [M^{0} L^{1} T^{0} ] = [M^{1} L^{2} T^{-2} ].$

$Therefore, work is dimensionally represented as [M^{1} L^{2} T^{-2}].$

Kinetic Energy:

Kinetic energy of an object is the measure of the work an object can do by virtue of its motion.

As a scalar quantity, kinetic energy can only be fully defined by its magnitude.

The kinetic energy equation is given as:

kinetic energy = $1/2mv^{2}$

Where,  m = mass

             v = velocity

Dimensional formula of Kinetic energy:

The dimensional formula of Kinetic Energy is given by,

             $[M^{1} L^{2} T^{-2}]$

Where,

• M = Mass
• L = Length
• T = Time

Derivation:

$Kinetic energy (K.E) = [Mass * Velocity^{2} ] * 2^{-1} . . . . . (1)$

$The dimensional formula of Mass = [M ^{1} L ^{0} T^{0} ] . . . . (2)$

$Since, Velocity = Distance * Time^{-1} = [L] * [T]^{-1}$

∴ $The dimensional formula of velocity = [M0 L1 T-1] . . . . (3)$

On substituting equation (2) and (3) in equation (1) we get,

$Kinetic energy = [Mass * Velocity^{2} ] * 2^{-1}$

$Or, K.E = [M^{1} L^{0} T^{0} ] * [M^{0} L^{1} T^{-1} ]^{2} = [M^{1} L^{2} T^{-2} ]$

$Therefore, Kinetic Energy is dimensionally represented as [M^{1} L^{2} T^{-2} ].$

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