Elasticity & SHM — JEE Main PYQs

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A: Steel is used in the construction of buildings and bridges.

Reason R: Steel is more elastic and its elastic limit is high.

In the light of above statements, choose …

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: A pendulum clock when taken to Mount Everest becomes fast.

Reason R: The value of $\mathbf{g}$ (acceleration due to gravity) is less at Mount Everest than its va …

A mass $m$ attached to free end of a spring executes SHM with a period of 1s. If the mass is increased by 3 kg the period of oscillation increases by one second, the value of mass $m$ is ____ kg.

T is the time period of simple pendulum on the earth's surface. Its time period becomes xT when taken to a height R (equal to earth's radius) above the earth's surface. Then, the value of $x$ will be:

Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is 100 g. The time period of the mot …

As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of $45^{\circ }$ with the load axis. The length of wire is 62.8 cm and its diameter is 4 …

A particle executes simple harmonic motion between $\mathrm{x}=-\mathrm{A}$ and $\mathrm{x}=+\mathrm{A}$. If time taken by particle to go from $x=0$ to $\frac{\mathrm{A}}{2}$ is 2 s ; then time taken by particle in going from $x=\frac{A}{2}$ to $A$ is :

A particle of mass 250 g executes a simple harmonic motion under a periodic force $\mathrm{F}=(-25\mathrm{x})\mathrm{N}$. The particle attains a maximum speed of $4\mathrm{m}/\mathrm{s}$ during its oscillation. The amplitude of the motion is ______ cm.

For a simple harmonic motion in a mass spring system shown, the surface is frictionless. When the mass of the block is 1 kg, the angular frequency is ${\omega }_1$. When the mass block is 2 kg the angular frequency is ${\omega }_2$. The ratio ${\omega }_2/{\omega }_1$ is :

A force is applied to a steel wire 'A', rigidly clamped at one end. As a result elongation in the wire is 0.2 mm. If same force is applied to another steel wire 'B' of double the length and a diameter 2.4 times that of the wire 'A', the elongation in the wire 'B' will be (wires h …

The velocity of a particle executing SHM varies with displacement $(\mathrm{x})$ as $4{\mathrm{v}}^2=50-{\mathrm{x}}^2$. The time period of oscillations is $\frac{x}{7}s$. The value of $x$ is \ldots\ldots.. $($ Take $\pi =\frac{22}{7})$

Choose the correct relationship between Poisson ratio ( $\sigma$ ). bulk modulus ( K ) and modulus of rigidity $(\eta )$ of a given solid object:

The general displacement of a simple harmonic oscillator is $x=A\sin \omega t$. Let T be its time period. The slope of its potential energy (U) - time (t) curve will be maximum when $t=\frac{T}{\beta }$. The value of $\beta$ is ______.

The maximum potential energy of a block executing simple harmonic motion is 25 J. A is amplitude of oscillation. At A/2, the kinetic energy of the block is

A thin rod having a length of 1 m and area of cross-section $3\times 10^{-6}$ m${}^2$ is suspended vertically from one end. The rod is cooled from $210°C$ to $160°C$. After cooling, a mass M is attached at the lower end of the rod such that the length of rod again becomes 1 m. You …

In the figure given below, a block of mass $M=490$ g placed on a frictionless table is connected with two springs having same spring constant ($K=2$ N m${}^{-1}$). If the block is horizontally displaced through 'X' m then the number of complete oscillations it will make in $14\pi$ …

Under the same load, wire A having length 5.0 m and cross section $2.5\times 10^{-5}{\mathrm{m}}^2$ stretches uniformly by the same amount as another wire B of length 6.0 m and a cross section of $3.0\times 10^{-5}{\mathrm{m}}^2$ stretches. The ratio of the Young's modulus …

The Young's modulus of a steel wire of length 6 m and cross-sectional area $3{\mathrm{mm}}^2$, is $2\times 10^{11}\mathrm{N}/{\mathrm{m}}^2$. The wire is suspended from its support on a given planet. A block of mass 4 kg is attached to the free end of the wire. The accelerat …

Choose the correct length $(L)$ versus square of time period $(T^2)$ graph for a simple pendulum executing simple harmonic motion.

A block is fastened to a horizontal spring. The block is pulled to a distance $\mathrm{x}=10\mathrm{cm}$ from its equilibrium position (at $\mathrm{x}=0$) on a frictionless surface from rest. The energy of the block at $\mathrm{x}=5$ cm is 0.25 J. The spring constant of the spr …

The speed of a transverse wave passing through a string of length 50 cm and mass 10 g is $60{\mathrm{ms}}^{-1}$. The area of cross-section of the wire is $2.0{\mathrm{mm}}^2$ and its Young's modulus is $1.2\times 10^{11}{\mathrm{Nm}}^{-2}$. The extension of the wire over its na …

The metallic bob of simple pendulum has the relative density 5. The time period of this pendulum is 10 s. If the metallic bob is immersed in water, then the new time period becomes $5\sqrt{x}$ s. The value of $x$ will be ______.

The force required to stretch a wire of cross-section $1{\mathrm{cm}}^2$ to double its length will be :
(Given Young's modulus of the wire $=2\times 10^{11}\mathrm{N}/{\mathrm{m}}^2$)

A string of area of cross-section $4{\mathrm{mm}}^2$ and length 0.5 is connected with a rigid body of mass 2 kg. The body is rotated in a vertical circular path of radius 0.5 m. The body acquires a speed of $5\mathrm{m}/\mathrm{s}$ at the bottom of the circular path. Strain …

The potential energy of a particle of mass 4 kg in motion along the x-axis is given by $U=4(1-\cos 4x)$ J. The time period of the particle for small oscillation $(\sin \theta \simeq \theta )$ is $\left(\frac{\pi }{K}\right)$ s. The value of $K$ is ____

Two identical positive charges Q each are fixed at a distance of '2a' apart from each other. Another point charge ${\mathrm{q}}_0$ with mass 'm' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge …

A mass 0.9 kg, attached to a horizontal spring, executes SHM with an amplitude ${\mathrm{A}}_1$. When this mass passes through its mean position, then a smaller mass of 124 g is placed over it and both masses move together with amplitude ${\mathrm{A}}_2$. If the ratio …

A square aluminium (shear modulus is $25\times 10^9{\mathrm{Nm}}^{-2}$) slab of side 60 cm and thickness 15 cm is subjected to a shearing force (on its narrow face) of $18.0\times 10^4\mathrm{N}$. The lower edge is riveted to the floor. The displacement of the upper edge i …

In figure (A), mass '2m' is fixed on mass 'm' which is attached to two springs of spring constant k. In figure (B), mass 'm' is attached to two spring of spring constant 'k' and '2k'. If mass 'm' in (A) and (B) are displaced by distance 'x' horizontally and then released, then ti …

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 5 cm. Another wire of the same material of length 4L and radius 4r is pulled by a force 4F under same conditions. The increase in length o …

The area of cross section of the rope used to lift a load by a crane is $2.5\times 10^{-4}$ m${}^2$. The maximum lifting capacity of the crane is 10 metric tons. To increase the lifting capacity of the crane to 25 metric tons, the required area of cross section of the rope should …

A uniform heavy rod of mass 20 kg, Cross sectional area $0.4{\mathrm{m}}^2$ and length 20 m is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is $\mathrm{x}\times 10^{-9}\mathrm{m}$. The value of x is ______. …

As per given figures, two springs of spring constants K and 2K are connected to mass m. If the period of oscillation in figure (a) is 3 s, then the period of oscillation in figure (b) will be $\sqrt{\mathrm{x}}$ s. The value of $x$ is ______.

A steel wire of length $3.2\mathrm{m}$ (${\mathrm{Y}}_{\mathrm{S}}=2.0\times 10^{11}{\mathrm{Nm}}^{-2}$) and a copper wire of length 4.4 M ( ${\mathrm{Y}}_{\mathrm{C}}=1.1\times 10^{11}{\mathrm{Nm}}^{-2}$ ), both of radius 1.4 mm are connected end to end. When stretched by a …

In an experiment to determine the Young's modulus, steel wires of five different lengths ($1,2,3,4$ and 5 m) but of same cross section ($2{\mathrm{mm}}^2$) were taken and curves between extension and load were obtained. The slope (extension/load) of the curves were plotted with …

The length of a seconds pendulum at a height $h=2R$ from earth surface will be:
(Given: $R=$ Radius of earth and acceleration due to gravity at the surface of earth $g={\pi }^2{m/s}^2$)

When a particle executes simple Harmonic motion, the nature of graph of velocity as function of displacement will be :

The equation of a particle executing simple harmonic motion is given by $x=\sin \pi \left(t+\frac{1}{3}\right)m$. At $\mathrm{t}=1\mathrm{s}$, the speed of particle will be
(Given : $\pi =3.14$ )

A particle executes simple harmonic motion. Its amplitude is 8 cm and time period is 6 s. The time it will take to travel from its position of maximum displacement to the point corresponding to half of its amplitude, is ______ s.

The motion of a simple pendulum executing S.H.M. is represented by following equation.
$\mathrm{Y}=\mathrm{A}\sin (\pi \mathrm{t}+\varphi )$, where time is measured in second.

The length of pendulum is :

A wire of length L is hanging from a fixed support. The length changes to $L_1$ and $L_2$ when masses 1 kg and 2 kg are suspended respectively from its free end. Then the value of L is equal to:

A body is performing simple harmonic with an amplitude of 10 cm . The velocity of the body was tripled by air Jet when it is at 5 cm from its mean position. The new amplitude of vibration is $\sqrt{\mathrm{x}}$ cm. The value of x is ______.

Time period of a simple pendulum in a stationary lift is ' T '. If the lift accelerates with $\frac{\mathrm{g}}{6}$ vertically upwards then the time period will be :
(where $\mathrm{g}=$ acceleration due to gravity)

The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of $5\times 10^{-4}$ is ____ kJ/m³. Assume that material is elastic upto the linear strain of $5\times 10^{-4}$.

The elongation of a wire on the surface of the earth is $10^{-4}$ m. The same wire of same dimensions is elongated by $6\times 10^{-5}$ m on another planet. The acceleration due to gravity on the planet will be ____ m/s². (Take acceleration due to gravity on the surface of earth …

The displacement of simple harmonic oscillator after 3 seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is :

If the length of a wire is made double and radius is halved of its respective values. Then, the Young's modules of the material of the wire will :

The time period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination $\alpha$, is given by :

The bulk modulus of a liquid is $3\times 10^{10}{\mathrm{Nm}}^{-2}$. The pressure required to reduce the volume of liquid by $2\%$ is :

Two massless springs with spring constants 2 k and 9 k , carry 50 g and 100 g masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be :