Elasticity & SHM — JEE Main PYQs

A simple pendulum doing small oscillations at a place $R$ height above earth surface has time period of ${\mathrm{T}}_1=4\mathrm{s}$. ${\mathrm{T}}_2$ would be it's time period if it is brought to a point which is at a height 2$R$ from earth surface. Choose the correct relation …

The density and breaking stress of a wire are $6\times 10^4\mathrm{kg}/{\mathrm{m}}^3$ and $1.2\times 10^8\mathrm{N}/{\mathrm{m}}^2$ respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is $\frac{1}{3}$ of the …

A particle is doing simple harmonic motion of amplitude 0.06 m and time period 3.14 s. The maximum velocity of the particle is ______ cm/s.

An object of mass 0.2 kg executes simple harmonic motion along x axis with frequency of $\left(\frac{25}{\pi }\right)$ Hz. At the position $x=0.04$ m the object has kinetic energy 0.5 J and potential energy 0.4 J. The amplitude of oscillation is _____ cm.

Two persons pull a wire towards themselves. Each person exerts a force of 200 N on the wire. Young's modulus of the material of wire is $1\times 10^{11}\mathrm{N}{\mathrm{m}}^{-2}$. Original length of the wire is 2 m and the area of cross section is $2{\mathrm{cm}}^2$. T …

The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of $4\mathrm{m},2{\mathrm{ms}}^{-1}$ and $16{\mathrm{ms}}^{-2}$ at a certain instant. The amplitude of the motion is $\sqrt{\mathrm{x}}\mathrm{m}$ where x …

A particle of mass 0.50 kg executes simple harmonic motion under force $\mathrm{F}=-50\left({\mathrm{Nm}}^{-1}\right)\mathrm{x}$. The time period of oscillation is $\frac{x}{35}s$. The value of $x$ is ................
(Given $\pi =\frac{22}{7}$ )

A wire of length L and radius r is clamped at one end. If its other end is pulled by a force F, its length increases by $l$. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in lengt …

Two metallic wires P and Q have same volume and are made up of same material. If their area of cross sections are in the ratio $4:1$ and force ${\mathrm{F}}_1$ is applied to P, an extension of $\Delta l$ is produced. The force which is required to produce same extension in …

A simple harmonic oscillator has an amplitude A and time period $6\pi$ second. Assuming the oscillation starts from its mean position, the time required by it to travel from $\mathrm{x}=\mathrm{A}$ to $\mathrm{x}=\frac{\sqrt{3}}{2}\mathrm{A}$ will be $\frac{\pi }{x}s$, …

A particle executes simple harmonic motion with an amplitude of 4 cm. At the mean position, velocity of the particle is $10\mathrm{cm}/\mathrm{s}$. The distance of the particle from the mean position when its speed becomes $5\mathrm{cm}/\mathrm{s}$ is …

If average depth of an ocean is 4000 m and the bulk modulus of water is $2\times 10^9{\mathrm{Nm}}^{-2}$, then fractional compression $\frac{\Delta V}{V}$ of water at the bottom of ocean is $\alpha \times 10^{-2}$. The value of $\alpha$ is ______ (Given, …

When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is $\frac{\mathrm{X}}{8}$, where $\mathrm{x}=$ $\_\_\_\_$.

The depth below the surface of sea to which a rubber ball be taken so as to decrease its volume by $0.02\%$ is ____ m.
(Take density of sea water $=10^3{\mathrm{kgm}}^{-3}$, Bulk modulus of rubber $=9\times 10^8{\mathrm{Nm}}^{-2}$, and …

A particle performs simple harmonic motion with amplitude A. Its speed is increased to three times at an instant when its displacement is $\frac{2\mathrm{A}}{3}$. The new amplitude of motion is $\frac{\mathrm{nA}}{3}$. The value of n is ____.

A mass m is suspended from a spring of negligible mass and the system oscillates with a frequency $f_1$. The frequency of oscillations if a mass 9 m is suspended from the same spring is $f_2$. The value of $\frac{f_1}{f_2}$ is ____.

One end of a metal wire is fixed to a ceiling and a load of 2 kg hangs from the other end. A similar wire is attached to the bottom of the load and another load of 1 kg hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will …

With rise in temperature, the Young's modulus of elasticity

If R is the radius of the earth and the acceleration due to gravity on the surface of earth is $g={\pi }^2\mathrm{m}/{\mathrm{s}}^2$, then the length of the second's pendulum at a height $\mathrm{h}=2\mathrm{R}$ from the surface of earth will be,:

A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is 4 m, then the time period of small oscillations will be $\_\_\_\_$ s. [take $\mathrm{g}={\pi }^2{\mathrm{ms}}^{-2}$]

Young's modules of material of a wire of length ' L ' and cross-sectional area A is Y . If the length of the wire is doubled and cross-sectional area is halved then Young's modules will be :

Each of three blocks $\mathrm{P},\mathrm{Q}$ and R shown in figure has a mass of 3 kg . Each of the wire $A$ and $B$ has cross-sectional area $0.005{\mathrm{cm}}^2$ and Young's modulus $2\times 10^{11}\mathrm{N}{\mathrm{m}}^{-2}$. Neglecting friction, the longitud …

Two blocks of mass 2 kg and 4 kg are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is $4.0\times 10^{-5}$ m and Young's modulus of the metal is $2.0\times 10^{11}\mathrm{N}/{\mathrm{m}}^2$. The longitudinal strain developed in t …

The time period of simple harmonic motion of mass M in the given figure is $\pi \sqrt{\frac{\alpha M}{5K}}$, where the value of $\alpha$ is ______.

Given below are two statements:
Assertion (A): The property of a body, by virtue of which it tends to regain its original shape when the external force is removed, is Elasticity.
Reason (R): The restoring force depends upon the bonded inter-atomic and inter-molecular force of t …

For particle P revolving round the centre O with radius of circular path r and angular velocity $\omega$, as shown in below figure, the projection of OP on the x-axis at time t is

An aluminium rod with Young's modulus $Y=7.0\times 10^{10}\mathrm{N}/{\mathrm{m}}^2$ undergoes elastic strain of $0.04\%$. The energy per unit volume stored in the rod in SI unit is:

A metal block of mass $m$ is suspended from a rigid support through a metal wire of diameter 14 mm. The tensile stress developed in the wire under equilibrium state is $7\times 10^5{\mathrm{Nm}}^{-2}$. The value of mass $m$ is ______ kg.
(Take, …

A simple pendulum with length 100 cm and bob of mass 250 g is executing S.H.M. of amplitude 10 cm. The maximum tension in the string is found to be $\frac{x}{40}$ N. The value of x is ____.

For a periodic motion represented by the equation
$\mathrm{Y}=\sin \omega \mathrm{t}+\cos \omega \mathrm{t}$
The amplitude of the motion is

Young's moduli of the material of wires A and B are in the ratio of $1:4$, while its area of cross sections are in the ratio of $1:3$. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires $A$ and $B$ will be in the rati …

A rectangular block of mass 5 kg attached to a horizontal spiral spring executes simple harmonic motion of amplitude 1 m and time period 3.14 s . The maximum force exerted by spring on block is ____ N.

A particle executes S.H.M. of amplitude A along $x$-axis. At $t=0$, the position of the particle is $\mathrm{x}=\frac{\mathrm{A}}{2}$ and it moves along positive x-axis. The displacement of particle in time $t$ is $\mathrm{x}=\mathrm{A}\sin (\omega \mathrm{t}+\delta )$, …

Two wires each of radius 0.2 cm and negligible mass, one made of steel and other made of brass are loaded as shown in the figure. The elongation of the steel wire is $\_\_\_\_$ $\times 10^{-6}\mathrm{m}$. [Young's modulus for steel $=2\times 10^{11}{\mathrm{Nm}}^{-2}$ and …

The variation of kinetic energy (KE) of a particle executing simple harmonic motion with the displacement ( x ) starting from mean position to extreme position (A) is given by

The length of wire becomes ${\ell }_1$ and ${\ell }_2$ when 100 N and 120 N tensions are applied respectively. If ${\ell }_2=\frac{11}{10}{\ell }_1$, the natural length of wire will be $\frac{1}{x}{\ell }_1$. Here the value of $x$ is ______.

A particle is executing Simple Harmonic Motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be:

A compass needle oscillates 20 times per minute at a place where the dip is $30^{\circ }$ and 30 times per minute where the dip is $60^{\circ }$. The ratio of total magnetic field due to the earth at two place respectively is $\frac{4}{\sqrt{x}}$. The value of $x$ is

Which graph represents the difference between total energy and potential energy of a particle executing SHM Vs it's distance from mean position?

The elastic potential energy stored in a steel wire of length 20 m stretched through 2 cm is 80 J. The cross sectional area of the wire is ______ mm${}^2$.
(Given, $Y=2.0\times 10^{11}$ Nm${}^{-2}$)

At a given point of time the value of displacement of a simple harmonic oscillator is given as $y=A\cos (30^0)$. If amplitude is 40 cm and kinetic energy at that time is 200 J, the value of force constant is $1.0\times 10^x$ Nm${}^{-1}$. The value of $x$ is ______.

A particle executes SHM of amplitude A. The distance from the mean position when its's kinetic energy becomes equal to its potential energy is :

In a linear simple harmonic motion (SHM)
(A) Restoring force is directly proportional to the displacement.
(B) The acceleration and displacement are opposite in direction.
(C) The velocity is maximum at mean position.
(D) The acceleration is minimum at extreme points.

Choose the …

A wire of length 'L' and radius 'r' is clamped rigidly at one end. When the other end of the wire is pulled by a force f, its length increases by '$\ell$'. Another wire of same material of length '2L' and radius '2r' is pulled by a force '2f'. Then the increase in its length will …

A mass m is attached to two springs as shown in figure. The spring constants of two springs are $K_1$ and $K_2$. For the frictionless surface, the time period of oscillation of mass $m$ is

A steel rod has a radius of 20 mm and a length of 2.0 m. A force of 62.8 kN stretches it along its length. Young's modulus of steel is $2.0\times 10^{11}\mathrm{N}/{\mathrm{m}}^2$. The longitudinal strain produced in the wire is $\_\_\_\_$ $\times 10^{-5}$

A certain pressure ' $P$ ' is applied to 1 litre of water and 2 litre of a liquid separately. Water gets compressed to $0.01\%$ whereas the liquid gets compressed to $0.03\%$. The ratio of Bulk modulus of water to that of the liquid is $\frac{3}{x}$. The value of $x$ …

The amplitude of a particle executing SHM is 3 cm. The displacement at which its kinetic energy will be 25% more than the potential energy is: ______ cm.

A 100 m long wire having cross-sectional area 6.25 $\times 10^{-4}{\mathrm{m}}^2$ and Young's modulus is $10^{10}{\mathrm{Nm}}^{-2}$ is subjected to a load of 250 N , then the elongation in the wire will be :

A block of mass 2 kg is attached with two identical springs of spring constant $20\mathrm{N}/\mathrm{m}$ each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibr …