PhysicsTwo cylinders A and B of the same materials have same length. Their radii being in the ratio of 1 : 2 respectively. The two are joined end to end as shown in the figure. The upper end of A is rigidly fixed. The lower end of B is twisted through an angle θ , the angle of twist of the cylinder A is :

Two cylinders A and B of the same materials have same length. Their radii being in the ratio of 1 : 2 respectively. The two are joined end to end as shown in the figure. The upper end of A is rigidly fixed. The lower end of B is twisted through an angle θ , the angle of twist of the cylinder A is :

  1. A

    1516θ

  2. B

    1615θ

  3. C

    1617θ

  4. D

    1716θ

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    Solution:

    We know that restoring torque,

    T=GθπR42L

    Since T, G, and L are constant for both cylinders,

    θ1R4

    θAθB=RBRA4

    θAθB=24

    θA=16θB

    Now as,

    θA+θB=θ

    θA+θA16=θ

    17θA16=θ

    θA=16θ17

    Hence the correct answer is 16θ17.

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