The dimensional formula of the effective tors | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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 $[M^1 L^2 T^{-2}]$.

List-$I$	List-$II$
$(A)$ Angular momentum	$(I)$ $[ML^2T^{-1}]$
$(B)$ Torque	$(II)$ $[ML^2T^{-2}]$
$(C)$ Stress	$(III)$ $[ML^{-1}T^{-2}]$
$(D)$ Pressure gradient	$(IV)$ $[ML^{-2}T^{-2}]$

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

Similar Questions

The dimensional formula $M L^{-1} T^{-2}$ does not represent which of the following physical quantities?

Which of the following is a unitless quantity?

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

List-$I$ List-$II$

$(A)$ Angular momentum $(I)$ $[ML^2T^{-1}]$

$(B)$ Torque $(II)$ $[ML^2T^{-2}]$

$(C)$ Stress $(III)$ $[ML^{-1}T^{-2}]$

$(D)$ Pressure gradient $(IV)$ $[ML^{-2}T^{-2}]$

Choose the correct answer from the options given below:

The dimensional formula for volume elasticity is:

Dimensional formula for activity of radioactive substance is

Vedclass Test Series

Exam Paper Generator

Online Exam Module