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(A) To find the pair with different dimensions,we analyze each option:$A$. Linear momentum = $	ext{Mass} 	imes 	ext{Velocity} = [M L T^{-1}]$. Mome

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Linear momentum and moment of a force

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(A) To find the pair with different dimensions,we analyze each option:$A$. Linear momentum = $	ext{Mass} 	imes 	ext{Velocity} = [M L T^{-1}]$. Moment of a force (Torque) = $	ext{Force} 	imes 	ext{Distance} = [M L T^{-2}] 	imes [L] = [M L^2 T^{-2}]$. These have different dimensions.$B$. Planck's constant $(h)$ has dimensions $[M L^2 T^{-1}]$. Angular momentum $(L = mvr)$ has dimensions $[M] 	imes [L T^{-1}] 	imes [L] = [M L^2 T^{-1}]$. These have the same dimensions.$C$. Pressure = $	ext{Force} / 	ext{Area} = [M L T^{-2}] / [L^2] = [M L^{-1} T^{-2}]$. Modulus of elasticity = $	ext{Stress} / 	ext{Strain} = [M L^{-1} T^{-2}] / [1] = [M L^{-1} T^{-2}]$. These have the same dimensions.$D$. Torque = $	ext{Force} 	imes 	ext{Distance} = [M L^2 T^{-2}]$. Potential energy = $	ext{Work} = [M L^2 T^{-2}]$. These have the same dimensions.Therefore,the correct option is $A$.

List-$I$	List-$II$
$(A)$ Torque	$(I)$ $kg\,m^{-1}\,s^{-2}$
$(B)$ Energy density	$(II)$ $kg\,m\,s^{-1}$
$(C)$ Pressure gradient	$(III)$ $kg\,m^{-2}\,s^{-2}$
$(D)$ Impulse	$(IV)$ $kg\,m^2\,s^{-2}$

List-$I$	List-$II$
$A$. Spring constant	$I$. $ML^2 T^{-2} K^{-1}$
$B$. Thermal conductivity	$II$. $ML^0 T^{-2}$
$C$. Boltzmann constant	$III$. $ML^2 T^{-3} A^{-2}$
$D$. Inductive reactance	$IV$. $MLT^{-3} K^{-1}$

In the following list,the only pair which has different dimensions is

Similar Questions

Match List-$I$ with List-$II$.

List-$I$ List-$II$

$(A)$ Torque $(I)$ $kg\,m^{-1}\,s^{-2}$

$(B)$ Energy density $(II)$ $kg\,m\,s^{-1}$

$(C)$ Pressure gradient $(III)$ $kg\,m^{-2}\,s^{-2}$

$(D)$ Impulse $(IV)$ $kg\,m^2\,s^{-2}$

Choose the correct answer from the options given below:

Select the pair from the following that does not have the same dimensions.

The units of length,velocity,and force are doubled. Which of the following is the correct change in the other units?

If the unit of force and length each be increased by four times,then the unit of energy is increased by $...$ times.

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