The dimensional formula for strain is same as that ofA. ThrustB. AngleC. Modulus of elasticityD. Stress

Dimensional Formula for Strain
Strain is defined as the ratio of the change in length (ΔL\Delta L) to the original length (LL):
Strain=ΔLL\text{Strain} = \frac{\Delta L}{L}
Since both ΔL\Delta L and LL have the same dimensional formula of length [L][L], strain is a dimensionless quantity. Therefore, the dimensional formula of strain is:
Dimensional formula of strain=[1]\text{Dimensional formula of strain} = [1]
This means strain has no units and is a pure number (dimensionless).
Analysis of the Options
Let’s analyze each option and its dimensional formula:
1. A. Thrust
o Thrust is the force exerted by a body, and its dimensional formula is the same as that of force:
[Thrust]=[MLT−2][\text{Thrust}] = [M L T^{-2}]
So, the dimensional formula of thrust is different from that of strain.
2. B. Angle
o Angle is a measure of the rotation or inclination between two lines, and it is dimensionless.
[Angle]=[1][\text{Angle}] = [1]
Since strain is also dimensionless, the dimensional formula for strain is the same as for angle.
3. C. Modulus of Elasticity
o The modulus of elasticity (EE) is the ratio of stress to strain. Stress has the dimensional formula [ML−1T−2][M L^{-1} T^{-2}], and strain is dimensionless.
[E]=[ML−1T−2][1]=[ML−1T−2][E] = \frac{[M L^{-1} T^{-2}]}{[1]} = [M L^{-1} T^{-2}]
The dimensional formula of the modulus of elasticity is different from that of strain.
4. D. Stress
o Stress is defined as force per unit area, and its dimensional formula is:
[Stress]=[MLT−2][L2]=[ML−1T−2][\text{Stress}] = \frac{[M L T^{-2}]}{[L^2]} = [M L^{-1} T^{-2}]
The dimensional formula of stress is also different from that of strain.
The dimensional formula for strain is the same as that of Angle.
Correct option: B.