Time Period of Pendulum — Prelims Questions

A simple pendulum has a time period $T$ on the Earth's surface. If its length is increased by $21$, what will be the new time period?

A simple pendulum of length $L$ has a time period $T$. If the bob is replaced by a heavier bob of double the mass, what will be the new time period?

A simple pendulum is suspended from the ceiling of a lift. If the lift accelerates upwards with an acceleration of $g/2$, what will be the new time period of the pendulum in terms of its original time period $T$?

A pendulum clock keeps correct time at a temperature of $20^circ\text{C}$. The coefficient of linear expansion of the pendulum rod is $alpha = 1.2 \times 10^{-5},\text{/}^circ\text{C}$. If the temperature rises to $40^circ\text{C}$, how many seconds will the clock lose or gain in one day?

A simple pendulum is oscillating in a tank of water. If the density of the bob is $ho_b$ and the density of water is $ho_w$, how does its time period change compared to oscillating in air?

A simple pendulum of length $1,\text{m}$ has a time period of $2,\text{s}$ on Earth. If it is taken to a planet where the acceleration due to gravity is $4$ times that on Earth, what will be its new time period?

Which of the following statements about the time period of a simple pendulum is INCORRECT?