NEET Physics MCQs

A student attempts to derive the formula for the period of a simple pendulum using dimensional analysis. They correctly identify the relevant variables as length (L), mass (m), and gravitational acceleration (g). Which of the following represents a fundamental limitation they will encounter?

In an experiment to determine the acceleration due to gravity ($g$) using a simple pendulum, the length ($L$) of the pendulum is measured as 98.1 cm with a least count of 1 mm, and the time period ($T$) for 20 oscillations is measured as 40.2 s with a least count of 0.1 s. What is the fractional error in the calculated value of $g$? (Use $g = 4\pi^2L/T^2$)

The time period of a simple pendulum is given by $T = 2\pi\sqrt{\frac{l}{g}}$. Dimensional analysis can help deduce this relationship except for:

A simple pendulum swings back and forth. At its highest point, which type of energy is maximum?

A simple pendulum of length 'l' and mass 'm' is released from an angle 'θ' with the vertical. What is its velocity at the lowest point?

A simple pendulum of length $L$ oscillates with a time period $T$. If the bob is replaced with another bob of mass four times the original, and the amplitude is halved, the new time period will be:

Two simple pendulums, A and B, have lengths $L$ and $4L$ respectively. If the bob of pendulum A is displaced by a small angle $heta$ and released, what angle should the bob of pendulum B be displaced by to have the same maximum velocity as pendulum A?

A simple pendulum with a bob of mass $m$ and length $L$ is oscillating in a lift accelerating upwards with acceleration $a$. The effective acceleration due to gravity experienced by the pendulum is:

A simple pendulum of length $L$ has a time period $T$. If the length is increased by $\Delta L$ such that $\Delta L << L$, the change in time period $\Delta T$ is approximately:

A simple pendulum is oscillating with an amplitude $A$. At what displacement from the mean position is its kinetic energy equal to its potential energy?