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    When a clock's minute hand moves, its shaft twists slightly, generating a torque proportional to the angle of twist. What physical property determines
    Question

    When a clock's minute hand moves, its shaft twists slightly, generating a torque proportional to the angle of twist. What physical property determines the torque in the clock's shaft?

    A.

    Viscous friction in the mechanism

    B.

    Torsional stiffness of the shaft

    C.

    Moment of inertia of the shaft

    D.

    Angular velocity

    Correct option is B

    When the clock’s shaft twists by a small angle, it behaves like a torsional spring.The restoring torque τ is given by:τ=kt θwhere: kt= torsional stiffness of the shaft θ= angle of twistThus, the torque generated is directly proportional to the torsional stiffness, which depends on: Material’s shear modulus Shaft geometry (length and polar moment of inertia)\text{When the clock's shaft twists by a small angle, it behaves like a torsional spring.} \\[6pt]\text{The restoring torque } \tau \text{ is given by:} \\[6pt]\tau = k_t \, \theta \\[8pt]\text{where:} \\[4pt]\bullet \ k_t = \text{ torsional stiffness of the shaft} \\[2pt]\bullet \ \theta = \text{ angle of twist} \\[8pt]\text{Thus, the torque generated is directly proportional to the torsional stiffness, which depends on:} \\[6pt]\bullet \ \text{Material's shear modulus} \\[2pt]\bullet \ \text{Shaft geometry (length and polar moment of inertia)}​​

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