Question

Whatever dimension a generalized co-
ordinate has, the product of the
generalized force and generalized
displacement (co-ordinate) must have
the dimension of:
(A)
Force
(B)
Torque
(C)
Work
(D)
None of the above​

Answer 1

Answer:

(B) is the correct answer.

Explanation:

Torque is defined as the product of force and perpendicular distance from axis of rotation.

$\vec \tau=\vec r\times \vec F$

Then, clearly, the dimensions of torque will be the product of dimensions of displacement and force.

Dimension of displacecment = $[L]$

Dimensions of force = $[MLT^{-2}]$

Dimensions of the product of force and displacement = $[L]*[MLT^{-2}]$

$=[ML^2T^{-2}]$

which is the same as the dimensions of torque.

Dimensions of torque = $[ML^2T^{-2}]$

$\therefore$ (B) is the correct answer.

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