Question

A light rigid rod of length $L$ has a bob of mass $M$ attached to one of its ends just like a simple pendulum. Speed at the lowest point when it is inverted and released is

Answer 1

We can solve this question by the law of conservation of energy. Before that student should know what a simple pendulum is and the law of conservation of energy. A point mass ‘m’ attached to a string of length ‘l’ in which the end attached to the mass is free and the other end is suspended from fixed support is called a simple pendulum.

Complete step by step answer:
Law of conservation of energy states that we cannot create or destroy any form of energy. We can only convert the energy from one form to another. Law of conservation of energy states that the energy of a system is always constant.If the velocity of the bob is ‘v’ at the bottom of the pendulum then kinetic energy is defined as the energy that is produced by an object due to its motion.

When an object is set to acceleration, there is a definite need to apply certain forces. The application of force needs work, and after the work is done, the energy gets transferred to the object making it move at a constant velocity. Potential energy is the form of energy by virtue of which energy is stored in an object due to some position and relative to some other position at rest is known as potential energy.

Three types of energy effects are shown here viz: nuclear energy, chemical, and potential electrical. This can be measured based on the distance, height, or mass of the object. It is measured in Joules.According to the law of conservation of energy,
Potential energy = kinetic energy
i.e., potential energy at the top of the bob = kinetic energy at the bottom of the bob
therefore,
$2mgL = \dfrac{1}{2}m{v^2}$
Here potential energy $= mg2L$
${v^2} = 4gL$
$\Rightarrow v = \sqrt {4gL}$
$\therefore v = 2\sqrt {gL}$
Therefore, Speed at the lowest point when it is inverted and released is $2\sqrt {gL}$

Therefore, the correct answer is option C.

Note: The equation for the time period is $T = 2\pi \sqrt {\dfrac{L}{g}}$. By this, we see that the time period of a simple pendulum only depends on the length of the string and the gravity. Students should know what kinetic and potential energy is and its formula. They should know what law of conservation of energy states.