Simple pendulum and its time period — practice questions

Question 1 · 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 2 · 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 3 · 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 4 · 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