the dimensions of restoring torque per unit angular displacement are
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Answer:
L. MLT^-2
ML^2T^2
................
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The dimensions of restoring torque per unit angular displacement are [M¹L²T⁻²].
We have to find the dimensions of restoring torque per unit angular displacement.
Concepts :
- Torque : Torque is a measure of a force than can cause an object to rotate about its axis.
- mathematically, Torque is the vector product of position and force vectors.
- Hence, the dimensions of Torque is the dimensions of product of position and force. i.e., dimensions of rF.
- angular displacement is the change in angle of an object about its axis. It is dimensionless quantity.
Now, dimensions of torque per unit angular displacement = dimensions of torque/dimensions of angular displacement
= dimensions of rF/[M⁰L⁰T⁰]
= [L¹][M¹L¹T⁻²]/[M⁰L⁰T⁰]
= [M¹L²T⁻²]
Therefore the dimensions of restoring torque per unit angular displacement are [M¹L²T⁻²].
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