B M Sharma Solutions for Chapter: Linear And Angular Simple Harmonic Motion, Exercise 4: DPP

Two pendulums have time periods $T$ and $\frac{5T}{4}$. They start SHM at the same time from the mean position. What will be the phase difference between them after the bigger pendulum has completed one oscillation.

Two simple pendulum, first a bob of mass $M_1$ and length $L_1$ and second a bob of mass $M_2$ and length $L_2. M_1=M_2$ and $L_1=2L_2$. If the vibrational energy of both is same, then, which one is correct?

In case of a simple pendulum, time period versus length is depicted by,

A $U$ tube of uniform bore having cross-sectional area $A$ has been set-up vertically, with open ends facing up. Now $M$ gram of a liquid of density $d$ is poured into it. The column of liquid in this tube will oscillate with a period $T$ such that,

A horizontal platform with an object placed on it is executing SHM in the vertical direction. The amplitude of oscillation is $3.92\times {10}^{-3} \mathrm{m}$. What must be the least period of these oscillations so that the object is not detached from the platform?

The metallic bob of a simple pendulum has relative density $\rho$. The time period of this pendulum is $T$. If the metallic bob is immersed in water, then, the new time period is given by,

A brass cube of side $a$ and density $\sigma$ is floating in mercury of density $\rho$. If the cube is displaced a bit vertically, it executes SHM. Its time period will be,

A man weighing  $60 \mathrm{kg}$ stands on the horizontal platform of a spring balance. The platform starts executing simple harmonic motion of amplitude $0.1 \mathrm{m}$ and frequency $\frac{2}{\pi } \mathrm{Hz}$. Which of the following statements is correct?