Question

Which of the following pairs of physical quantities does not have same dimensional formula ?
(a) Work and Energy
(b) Force and torque
(c) Pressure and Stress
(d) Impulse and linear momentum
Quetion is based on given statement
Statement. The distance move by a particle with time r varies as S=r-31° +41 + 2 then​

Answer 1

Answer:

The answer is a option A

Answer 2

$\mathcal{\bold {ANSWER}}$ :

The pair of physical quantity which does not have the same dimensional formula is option (B) Force and torque

$\mathcal{\bold {EXPLANATION}}$ :

$\{\Rightarrow\}$$\mathbb{\bold {OPTION \ A}}$

We know that,

Work = Force * Displacement

Energy = mgh or Energy = 1/2 mv²

Hence,

[Work] = M L² T⁻²

[Energy] = M L² T⁻²

Therefore,

[Work] = [Energy]

$\{\Rightarrow\}$$\mathbb{\bold {OPTION \ B}}$

We know that,

Force = Mass * Acceleration

Torque = Force * Distance from centre

Hence,

[Force] = M L T⁻²

[Torque] = M L² T⁻²

Therefore,

[Force] ≠ [Torque]

$\{\Rightarrow\}$$\mathbb{\bold {OPTION \ C}}$

We know that,

Pressure = Force / Area

Stress = Force / Area

Hence,

[Pressure] = M L⁻¹ T⁻²

[Stress] = M L⁻¹ T⁻²

Therefore,

[Pressure] = [Stress]

$\{\Rightarrow\}$$\mathbb{\bold {OPTION \ D}}$

We know that,

Impulse = Δp = mv - mu = m(v-u)

Linear momentum = p = mv

Hence,

[Impulse] = M L T⁻¹

[Linear Momentum] = M L T⁻¹

Therefore,

[Impulse] = [Linear Momentum]