Properties of Matter Part 3

Modulus of Elasticity (Young's Modulus, E)
- Dimensional formula:
E=‌

‌ Stress ‌

‌ Strain ‌

- Stress = Force ∕ Area =‌

MLT−2

L2

=ML−1T−2
- Strain is dimensionless.
- So, dimensional formula of E :
[E]=ML−1T−2
Torque ( τ )
- Torque = Force × Distance
- τ=(MLT−2)×L=ML2T−2
- So, dimensional formula of τ :
[τ]=ML2T−2
‌

E

τ

=‌

ML−1T−2

ML2T−2

Canceling M and T−2 :
Thus, the dimensional formula of the required quantity is:
=L−1−2=L−3
[M0L−3T0]
Compare with MaLbTc
a=0,‌‌b=−3,‌‌c=0