Question:
A simple pendulum performing small oscillations at a height R above Earth's surface has a time period of \(T_1 = 4\) s. What would be its time period at a point which is at a height \(2R\) from Earth's surface?
A simple pendulum performing small oscillations at a height R above Earth's surface has a time period of \(T_1 = 4\) s. What would be its time period at a point which is at a height \(2R\) from Earth's surface?
Show Hint
The time period of a simple pendulum is independent of the height above Earth's surface for small oscillations.
Updated On: Apr 15, 2026
- \(T_1 = T_2\)
- \(2T_1 = 3T_2\)
- \(3T_1 = 2T_2\)
- \(2T_1 = T_2\)
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
The time period of a simple pendulum is given by the formula: \[ T = 2\pi \sqrt{\frac{L}{g}} \] Where \(L\) is the length of the pendulum and \(g\) is the acceleration due to gravity. At height \(R\) above Earth's surface, \(g\) is reduced slightly, but since we're dealing with small changes in height, the time period will remain approximately the same at a height \(2R\). Thus, \(T_1 = T_2\).
Was this answer helpful?
2
13
Top BITSAT Physics Questions
- Two point charges $-q$ and $+ q$ are located at point's $(0, 0, - a)$ and, $(0, 0, a)$ respectively. The electric potential at a point $(0, 9, z)$, where $z > a$ is
- Which of the following must be known in order to determine the power output of an automobile?
- A large drop of oil (density $0.8 \,g / cm ^{3}$ and viscosity $\eta_{0}$ ) floats up through a column of another liquid (density $1.2\, g / cm ^{3}$ and viscosity $\eta_{L}$ ). Assuming that the two liquids do not mix, the velocity with which the oil drop rises will depend on :
- A body is projected vertically upwards at time $ t = 0$ and it is seen at a height $H$ at time $t_1$ and $t_2$ second during its flight. The maximum height attained is ($g$ is acceleration due to gravity)
- At what point of a projectile motion, acceleration and velocity are perpendicular to each other ?
View More Questions
Top BITSAT simple harmonic motion Questions
- A particle of mass $m$ executes simple harmonic motion with amplitude a and frequency $n$. The average kinetic energy during its motion from the position of equilibrium to the end is.
- A particle on the trough of a wave at any instant will come to the mean position after a time : ($T =$ time period)
- The amplitude of a damped oscillator becomes $\left(\frac{1}{3}\right)rd$ in $2$ seconds. If its amplitude after $6$ seconds is $\frac{1}{n}$ times the original amplitude, the value of $n$ is
- The displacement of a particle is given at time $t$, by $x=A \sin (-2 \omega t)+B \sin ^{2} \omega t$ Then
- Two particles $P$ and $Q$ describe S.H.M. of same amplitude a, same frequency $f$ along the same straight line. The maximum distance between the two particles is $a \sqrt{2}$ The initial phase difference between the particle is
Top BITSAT Questions
- Two point charges $-q$ and $+ q$ are located at point's $(0, 0, - a)$ and, $(0, 0, a)$ respectively. The electric potential at a point $(0, 9, z)$, where $z > a$ is
- Which of the following must be known in order to determine the power output of an automobile?
- A large drop of oil (density $0.8 \,g / cm ^{3}$ and viscosity $\eta_{0}$ ) floats up through a column of another liquid (density $1.2\, g / cm ^{3}$ and viscosity $\eta_{L}$ ). Assuming that the two liquids do not mix, the velocity with which the oil drop rises will depend on :
- A body is projected vertically upwards at time $ t = 0$ and it is seen at a height $H$ at time $t_1$ and $t_2$ second during its flight. The maximum height attained is ($g$ is acceleration due to gravity)
- At what point of a projectile motion, acceleration and velocity are perpendicular to each other ?
View More Questions