Question

The value of the angle of twist at the clamped end of a rod is
(A) ${90^0}$
(B) ${180^0}$
(C) ${60^0}$
(D) ${0^0}$

Answer 1

Hint: - To solve this question, first we need to learn about the clamped end. A clamped end means the object is fixed or tightly secured at that end. The clamped end restricts any kind of motion (translational motion or rotational motion) at that point. So, we have to calculate the angle of twist at this clamped end.

Complete step by step solution:
The angle of twist is the angle through which the fixed end of the rod rotates with respect to the free end of the rod. The clamped end of the rod is rigidly fixed to a surface. Since it is fixed, the angle of twist at the clamped end will always be ${0^0}$.
The angle of twist is given by:
$\theta = \dfrac{{TL}}{{GJ}}$
$\theta$ is in radians but generally, it is converted to degrees, T is total torque (Nm), L is the length of segment (m), G is shear modulus (Gpa), and J is the polar moment of inertia (${m^4}$)

The correct option is (D).

Note: Angle of twist starts from ${0^0}$ increases linearly as we go from clamped end to free end of the rod. The angle of twist also depends upon torque applied. The rate of change of angle of the twist with respect to distance from the clamped end of the rod$(d\theta /dx)$ is called the rate of twist and used to find torque applied on the rod. If the rod is very rigid that is shear modulus is high, the angle of twist will be small and if the rod is flexible that is its shear modulus is small, the angle of twist will be more.