The problem states that an object experiences a torque $\tau$ and an angular acceleration $\alpha$. We need to find the dimensions of $\frac{\tau}{\alpha}$.

Applied MathematicsPhysicsTorqueMoment of InertiaDimensional Analysis
2025/6/26

1. Problem Description

The problem states that an object experiences a torque τ\tau and an angular acceleration α\alpha. We need to find the dimensions of τα\frac{\tau}{\alpha}.

2. Solution Steps

We know that torque τ\tau is given by
τ=Iα\tau = I \alpha,
where II is the moment of inertia and α\alpha is the angular acceleration.
Therefore,
τα=I\frac{\tau}{\alpha} = I.
The moment of inertia II is given by I=mr2I = mr^2, where mm is the mass and rr is the distance from the axis of rotation. Thus, the dimensions of II are [M][L2]=ML2[M][L^2] = ML^2.
Therefore, the dimensions of τα\frac{\tau}{\alpha} are ML2ML^2.

3. Final Answer

ML2ML^2
The answer is (2) ML2ML^2 .

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