Question:
The time period of a simple pendulum of length $l$ is $T$. If its length is increased to $4l$, its new time period will be
The time period of a simple pendulum of length $l$ is $T$. If its length is increased to $4l$, its new time period will be
Show Hint
Remember that for a simple pendulum, doubling the length results in a doubling of the time period due to the square root relationship in the formula.
Updated On: May 31, 2026
- $2T$
- $4T$
- $T/2$
- $T$
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Concept
The time period \( T \) 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.
Step 2: Meaning
This means that the time period depends on the square root of the length of the pendulum. If we increase the length, the time period will also increase proportionally according to this relationship.
Step 3: Analysis
Given: Original length: \( l \) Original time period: \( T = 2\pi \sqrt{\frac{l}{g}} \) When the length is increased to \( 4l \): \[T_{\text{new}} = 2\pi \sqrt{\frac{4l}{g}}\] We can simplify this expression: \[T_{\text{new}} = 2\pi \sqrt{4} \cdot \sqrt{\frac{l}{g}}\] \[T_{\text{new}} = 2\pi \cdot 2 \cdot \sqrt{\frac{l}{g}}\] \[T_{\text{new}} = 2 \cdot (2\pi \sqrt{\frac{l}{g}})\] \[T_{\text{new}} = 2T\] Thus, the new time period is twice the original time period.
Step 4: Conclusion
The time period of a simple pendulum increases proportionally with the square root of its length. When the length is quadrupled, the time period doubles. Final Answer: (A)
Was this answer helpful?
0
0
Top AP EAPCET Physics Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The radii of the two columns in a U - tube are r1 and r2. When a liquid of density p (angle of contact is $ 0{}^\circ $ ) is filled in it, the level difference of the liquid in the two arms is h. The surface tension of the liquid is: (g = acceleration due to gravity)
- A rigid metallic sphere is spinning around its own axis in the absence of external torque. If the temperature is raised, its volume increases by $9 \%$. The change in its angular speed is
View More Questions
Top AP EAPCET Pendulums Questions
- A simple pendulum is suspended in a car moving on a circular track of radius \( R \) with a uniform speed of \( \sqrt{1.732 g R} \). The pendulum is making small oscillations in a radial direction about its equilibrium position with a time period \( T \). If the car is at rest, the time period of the pendulum is:
- The time period of a simple pendulum is $T$ in air. When the bob is completely immersed in a non-viscous liquid of density $\rho / 10$ (where $\rho$ is the density of the bob), the new time period of oscillation is: [H] [width=0.5\linewidth]{86.png}
- The time period of a simple pendulum is $T$ in air. When the bob is completely immersed in a non-viscous liquid of density $\rho / 10$ (where $\rho$ is the density of the bob), the new time period of oscillation is:
- The time period of a simple pendulum of length $l$ is $T$. If its length is increased to $4l$, its new time period will be
Top AP EAPCET Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- The four quantum numbers of the valence electron of potassium are :
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
View More Questions