Q. 74.5( 13 Votes )

# Taking force, length and time to be the fundamental quantities find the dimensions of

A. density, B. pressure,

C. momentum and D. energy.

Answer :

A. Density is defined as the mass contained in per unit volume of a body.

We also know that force on a body can be given by the relation

Force (F) = mass (m) × acceleration (a)

So, by this definition, we can write

Dimensions of m =

Dimensions of v = [L^{3}]

Dimensions of d =

B. Pressure is defined as the amount of force exerted normally per unit area.

Dimensions of F = [F]

Dimensions of A = [L^{2}]

Dimensions of P =

C. Momentum is defined as the amount of motion contained in a moving body. Mathematically it is given as

Momentum(p) = mass(m) × velocity(v)

We also know that force on a body can be given by the relation

Force (F) = mass (m) × acceleration (a)

So, by this definition, we can write

Dimensions of m =

Dimensions of v =[LT^{-1}]

Dimensions of p =

D. Energy is defined as the amount of work a body has done or is capable of doing. For a body of mass m, moving with velocity v, the energy possessed due to its motion will be kinetic energy (a form of energy). Kinetic energy will be given by the relation,

Kinetic energy(E) = � m v^{2}

We also know that force on a body can be given by the relation

Force (F) = mass (m) × acceleration (a)

So, by this definition, we can write

Dimensions of m =

Dimensions of v^{2} = [L^{2}T^{-2}]

Dimensions of E =

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