Simple pendulum and its time period — NEET & JEE Questions

Question 1 · difficulty L1 · recall

For small oscillations, the time period of a simple pendulum of length l is

• A. $T=2\pi\sqrt{\frac{l}{g}}$
• B. $T=2\pi\sqrt{\frac{g}{l}}$
• C. $T=\frac{l}{g}$
• D. $T=2\pi lg$

Question 2 · difficulty L2 · understanding

For small-amplitude oscillations, the simple pendulum period is approximately independent of

• A. bob mass
• B. pendulum length
• C. local gravitational acceleration
• D. the square root of length

Question 3 · difficulty L2 · understanding

If the length of a simple pendulum is increased, its period

• A. increases
• B. decreases
• C. remains unchanged
• D. becomes zero

Question 4 · difficulty L2 · understanding

The standard simple-pendulum period formula is most accurate when the angular amplitude is

• A. small
• B. very large near 180 degrees
• C. irrelevant at all amplitudes
• D. exactly 90 degrees

Question 5 · difficulty L3 · understanding

Savitha, a XI standard student, while conducting an experiment to determine the effective length of a simple pendulum $L$, notes down the data of time taken to complete 30 oscillations as 60 s and hence calculates the length of the simple pendulum as: (Take $\pi^2=9.8$, and $g=9.8 \mathrm{~m} / \mathrm{s}^2$ )

• A. 0.75 m
• B. 1.5 m
• C. 2 m
• D. 1 m

Question 6 · difficulty L3 · understanding

If the mass of the bob in a simple pendulum is increased to thrice its original mass and its length is made half its original length, then the new time period of oscillation is $$\frac{x}{2}$$ times its original time period. Then the value of $$x$$ is:

• A. $$\sqrt{3}$$
• B. $$\sqrt{2}$$
• C. $$2 \sqrt{3}$$
• D. 4

Question 7 · difficulty L3 · understanding

A simple pendulum oscillating in air has a period of $$\sqrt{3} \mathrm{~s}$$. If it is completely immersed in non-viscous liquid, having density $$\left(\frac{1}{4}\right)^{\text {th }}$$ of the material of the bob, the new period will be :-

• A. $$2 \sqrt{3}$$ s
• B. $$\frac{2}{\sqrt{3}} \mathrm{~s}$$
• C. $$2 \mathrm{~s}$$
• D. $$\frac{\sqrt{3}}{2} \mathrm{~s}$$

Question 8 · difficulty L3 · understanding

Two pendulums of length 121 cm and 100 cm start vibrating in phase. At some instant, the two are at their mean position in the same phase. The minimum number of vibrations of the shorter pendulum after which the two are again in phase at the mean position is :

• A. 11
• B. 9
• C. 10
• D. 8

Question 9 · difficulty L4 · application

If the length of a simple pendulum is quadrupled at the same location, its period becomes

• A. twice
• B. four times
• C. half
• D. unchanged

Question 10 · difficulty L4 · application

A pendulum has period 2 s where $g=9.8\,\text{m s}^{-2}$. If taken to a place with smaller g but unchanged length, its period will

• A. increase
• B. decrease
• C. stay exactly 2 s
• D. become zero