Question

From the given options find Which of the following is true about initial situation and situation at maximum elongation?

(A) The orientation of spring in both positions should be perpendicular to each other
(B) Zero should be the maximum extension velocity
(C) At maximum extension as well as at initial position the velocity should be perpendicular to the spring
(D) At the maximum extension as well as at initial position the acceleration should be zero

Answer 1

The measure of deformation which occurs before a material breaks eventually when subjected to a tensile load is defined as the elongation. The length at breaking point defined as a percentage of its original length is also called the elongation. The velocity of the spring is equal to multiples of the angular velocity and the length of the spring. From the given diagram the spring is an extension at the perpendicular direction.

Complete answer:
The maximum elongation of the spring is that the block has an initial velocity of $2ms - 1$ in the downward direction if the spring is in a non-deformed shape.
From the given diagram,
Velocity ${\overrightarrow v _0} = \overrightarrow \omega \times {\overrightarrow l _0}$
Here,
${l_0}$ is the length of the string.
$\omega$ is the angular velocity of the particular mass $m$
$\therefore {v_0} = \omega {l_0}\sin \theta$
Therefore, velocity will be maximum when ${l_0}$ is equal to the maximum elongation length as well as when $\theta = 90$ means initial position perpendicular to the spring.
Hence, the correct answer is the velocity at maximum extension as well as at initial position should be perpendicular to spring.

Note:
Elongation is very important in manufacturing as it measures how much bending and shaping a material can withstand without breaking. The tensile stress required to produce a total elongation of $0.5\%$ is called the minimum yield strength. The maximum elongation is the angular separation between the sun and solar system body as observed from the earth.