The dimensional formula of the effective tors | vedclass

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Question

(B) The torsional constant $(k)$ for a spring or a wire is defined by the relation $	au = k	heta$,where $	au$ is the torque and $	heta$ is the ang

Vedclass · Accepted Answer

$M^1 L^2 T^{-2}$

Vedclass · Answer

(B) The torsional constant $(k)$ for a spring or a wire is defined by the relation $	au = k	heta$,where $	au$ is the torque and $	heta$ is the angular displacement in radians.Since $	heta$ is dimensionless,the dimensions of the torsional constant $(k)$ are the same as the dimensions of torque $(	au)$.Torque is defined as the product of force and perpendicular distance: $	au = F 	imes d$.The dimensional formula for force $(F)$ is $[M^1 L^1 T^{-2}]$.The dimensional formula for distance $(d)$ is $[L^1]$.Therefore,the dimensional formula for torque $(	au)$ is $[M^1 L^1 T^{-2}] 	imes [L^1] = [M^1 L^2 T^{-2}]$.Thus,the dimensional formula of the effective torsional constant is $[M^1 L^2 T^{-2}]$.

Column-$I$	Column-$II$
$(a)$ Viscous force	$(i)$ $[M^1 L^1 T^{-2}]$
$(b)$ Coefficient of viscosity	$(ii)$ $[M^1 L^{-1} T^{-1}]$
	$(iii)$ $[M^1 L^{-1} T^{-2}]$

The dimensional formula of the effective torsional constant of a spring is . . . . . . .

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Column-$I$ Column-$II$

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