Embibe Experts Solutions for Chapter: Simple Harmonic Motion, Exercise 2: Exercise 2

A hollow pendulum bob filled with water has a small hole at the bottom through which water escapes at a constant rate. Which of the following statements describes the variation of the time period $\left(T\right)$ of the pendulum as the water flows out?

There is a smooth fixed concave surface. A particle of mass $m$ is released from $P$. Find potential energy as a function of $\theta$. Radius of the surface is $R$.

A simple pendulum oscillates freely between points $A$ and $B$.

We now put a peg (nail) at some point $C$ as shown. As the pendulum moves from $A$ to the right, the string will bend at $C$ and the pendulum will go to its extreme point $D$. Ignoring friction, the point $D$,

A large number of random snapshots using a camera are taken of a particle in simple harmonic motion between $x=-x_0$ and $x=+x_0$ with origin $x=0$ as the mean position. A histogram of the total number of times the particle is recorded about a given position (event number) would most closely resemble,

A simple pendulum is attached to a block which slides without friction down an inclined plane $\left(ABC\right)$ having an angle of inclination $\alpha$ as shown while the block is sliding down the pendulum oscillates in such a way that at its mean position the direction of the string is,

A simple pendulum of length $l$ is made to oscillate with amplitude of $45$ degrees. The acceleration due to gravity is g. Let $T_0=2\mathrm{\pi }\sqrt{\frac{l}{g}}.$ The time period of oscillation of this pendulum will be

A light balloon filled with helium of density ${\rho }_{\mathrm{He}}$ is tied to a long light string of length $l$ and the string is attached to the ground. If the balloon is displaced slightly in the horizontal direction from the equilibrium and released then:

A potential is given by $V\left(x\right)=\frac{k{\left(x+a\right)}^2}{2}$ for $x<0$ and $V\left(x\right)=\frac{k{\left(x-a\right)}^2}{2}$ for $x>0$. Plot the schematic variation of oscillation period $\left(T\right)$ for a performing periodic motion in this potential as a function of its total energy $E$ is: