G L Mittal and TARUN MITTAL Solutions for Chapter: Simple Harmonic Motion, Exercise 2: NUMERICALS

The value of acceleration due to gravity on a planet is $\frac{1}{9}$  that of the earth. The time period of a simple pendulum on earth is $1 \sec$. Find its time period on the planet.

Two pendulums of length $100 \mathrm{cm}$and $110.25 \mathrm{cm}$  start oscillating in phase simultaneously. After how many oscillations, they will again be in phase?

The pendulum whose time period is $2 \sec$ is called seconds pendulum. What is length of the seconds pendulum on earth? On moon? The value of '$\mathrm{g}$' on earth is $9.8 {\mathrm{ms}}^{-2}$ and on the moon $\frac{1}{6}$ of that on earth.

The second pendulum is taken to a height, where the value of $\text{'}\mathrm{g}\text{'}$ is $4.36 {\mathrm{ms}}^{-2}$. What will be its new time period$?$

A simple pendulum whose length is $20 \mathrm{cm}$ is suspended from a ceiling of a lift which is rising up with an acceleration of $3.0 m {\mathrm{s}}^{-2}$. Calculate the time period of the pendulum.

If radius of earth is $6.4\times {10}^6\mathrm{m}$, Calculate periodic time of a simple pendulum of infinite length.

A small body of mass $0.1 \mathrm{kg}$ is executing S.H.M. of amplitude $1.0 \mathrm{m}$ and period $0.2 \sec$. Calculate the maximum force acting on it.

On pouring$10 \mathrm{g}$ mercury into a test tube of mass $8 g$ and external diameter $2 \mathrm{cm}$, the test tube floats vertically in the water. The test tube is pressed down into the water and left. Prove that the motion of the tube will be simple harmonic. Also find its time period.