Question

find the dimensions formal Formula for force and kinetic energy Full​

Answer 1

Answer:

Explanation:

For Force:-

Force=ma =[M] [LT-¹]= [MLT‐²]

For kinetic energy:-

Kinetic Energy =1/2mv²= [M] [LT‐¹]² = [ML²T‐²]

Answer 2

Explanation:

dimensions formal Formula for force:

Force = mass × acceleration

[F] = [M] × [L(T^−2)] = ML(T^−2)

dimensions Formula of Kinetic energy

Derivation, using algebra alone (and assuming constant acceleration). Start from the theorem of work-energy, then add in the second law of motion by Newton.

The dimensional formula of Kinetic Energy is expressed by below equation

[(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)

Subsequently, Velocity = Distance × Time^-1 = L × T^-1

Therefore, The dimensional formula of velocity = [(M^0) (L^1) (T^-1)] --------------------(3)

Now substitute equation (2) and (3) in equation (1) then we get,

⇒ K.E= [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)]

If kinetic energy is the energy of motion then the kinetic energy of an object in rest should naturally be zero. So we don't need the second term and the kinetic energy of an object is just

Hence, Kinetic Energy is dimensionally expressed as [(M^1) (L^2) (T^-2)].