Question

Given below is the plot of a potential energy function $\mathrm{U}\left(\mathrm{x}\right)$ for a system, in which a particle is in one dimensional motion, while a conservative force $\mathrm{F}\left(\mathrm{x}\right)$ acts on it. Suppose that ${\mathrm{E}}_{\text{mech }}=8 \mathrm{J}$, the incorrect statement for this system is :

JEE Main 2021 (27 Jul Shift 2)

Options

• A: at $\mathrm{x}>{\mathrm{x}}_4, \mathrm{K}.\mathrm{E}$. is constant throughout the region.
• B: at $\mathrm{x}<{\mathrm{x}}_1, \mathrm{K}.\mathrm{E}$. is smallest and the particle is moving at the slowest speed.
• C: at $\mathrm{x}={\mathrm{x}}_2, \mathrm{K}.\mathrm{E}$. is greatest and the particle is moving at the fastest speed.
• D: at $\mathrm{x}={\mathrm{x}}_3, \mathrm{K}.\mathrm{E}.=4 \mathrm{J}$

Question

An engine is attached to a wagon through a shock absorber of length $1.5 \mathrm{m}.$ The system with a total mass of $40,000 \mathrm{kg}$ is moving with a speed of $72 \mathrm{km} {\mathrm{h}}^{-1}$ when the brakes are applied to bring it to rest. In the process of the system being brought to rest, the spring of the shock absorber gets compressed by $1.0 \mathrm{m}$. If $90\%$ of energy of the wagon is lost due to friction, the spring constant is $\_\_\_\_\_\_\_\_\_\times {10}^5 \mathrm{N} {\mathrm{m}}^{-1}.$

JEE Main 2021 (01 Sep Shift 2)

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Question

As shown in the figure, a particle of mass $10 \mathrm{kg}$ is placed at a point $A.$ When the particle is slightly displaced to its right, it starts moving and reaches the point $B.$ The speed of the particle at $B$ is $x \mathrm{m} {\mathrm{s}}^{-1}$. (Take $\left.g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$ The value of $x$ to the nearest integer is

JEE Main 2021 (18 Mar Shift 1)

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Question

The potential energy $\left(U\right)$ of a diatomic molecule is a function dependent on $r$ (interatomic distance) as $U=\frac{\alpha }{r^{10}}-\frac{\beta }{r^5}-3$ where, $\alpha$ and $\beta$ are positive constants. The equilibrium distance between two atoms will be ${\left(\frac{2\alpha }{\beta }\right)}^{\frac{a}{b}},$ where $a=$______ .

JEE Main 2021 (25 Feb Shift 1)

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Question

Potential energy as a function of $r$ is given by $U=\frac{A}{r^{10}}-\frac{B}{r^5}$, where $r$ is the interatomic distance, $A$ and $B$ are positive constants. The equilibrium distance between the two atoms will be :

JEE Main 2022 (24 Jun Shift 2)

Options

• A: ${\left(\frac{A}{B}\right)}^{\frac{1}{5}}$
• B: ${\left(\frac{B}{A}\right)}^{\frac{1}{5}}$
• C: ${\left(\frac{2A}{B}\right)}^{\frac{1}{5}}$
• D: ${\left(\frac{B}{2A}\right)}^{\frac{1}{5}}$

Question

A body of mass $0.5 \mathrm{kg}$ travels on straight line path with velocity $v=\left(3x^2+4\right) \mathrm{m} {\mathrm{s}}^{-1}$. The net work done by the force during its displacement from $x=0$ to $x=2 \mathrm{m}$ is

JEE Main 2022 (25 Jul Shift 1)

Options

• A: $64 \mathrm{J}$
• B: $60 \mathrm{J}$
• C: $120 \mathrm{J}$
• D: $128 \mathrm{J}$

Question

Arrange the four graphs in descending order of total work done; where $W_1,W_2,W_3$ and $W_4$ are the work done corresponding to figure $a,b,c$ and $d$ respectively.

JEE Main 2022 (26 Jun Shift 2)

Options

• A: $W_3>W_2>W_1>W_4$
• B: $W_3>W_2>W_4>W_1$
• C: $W_2>W_3>W_4>W_1$
• D: $W_2>W_3>W_1>W_4$

Question

In the given figure, the block of mass $m$ is dropped from the point $\text{'}A\text{'}$. The expression for kinetic energy of block when it reaches point $\text{'}B\text{'}$ is

JEE Main 2022 (29 Jun Shift 2)

Options

• A: $mg{y}_0$
• B: $\frac{1}{2}mg{y}_0^2$
• C: $\frac{1}{2}mg{y}^2$
• D: $mg\left(y-y_0\right)$

Question

A ball of mass $100 \mathrm{g}$ is dropped from a height $h=10 \mathrm{cm}$ on a platform fixed at the top of a vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance $\frac{h}{2}$. The spring constant is _____ $\mathrm{N} {\mathrm{m}}^{-1}$
(Use $g=10{ \mathrm{m} \mathrm{s}}^{-2}$)

JEE Main 2022 (24 Jun Shift 1)

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Question

A block of mass '$m$' (as shown in figure) moving with kinetic energy $E$ compresses a spring through a distance $25 \mathrm{cm}$ when, its speed is halved. The value of spring constant of used spring will be $nE \mathrm{N} {\mathrm{m}}^{-1}$ for $n=$_____.

JEE Main 2022 (28 Jul Shift 1)

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Question

If a rubber ball falls from a height $h$ and rebounds upto the height of $h / 2$. The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are :

JEE Main 2024 (04 Apr Shift 1)

Options

• A: $50 \%, \sqrt{2 \mathrm{gh}}$
• B: $50 \%, \sqrt{\mathrm{gh}}$
• C: $40 \%, \sqrt{2 \mathrm{gh}}$
• D: $50 \%, \sqrt{\frac{\mathrm{gh}}{2}}$

Question

A body of $m \mathrm{~kg}$ slides from rest along the curve of vertical circle from point $A$ to $B$ in friction less path. The velocity of the body at $B$ is:
$\text { (given, } R=14 \mathrm{~m}, g=10 \mathrm{~m} / \mathrm{s}^2 \text { and } \sqrt{2}=1.4 \text { ) }$

JEE Main 2024 (04 Apr Shift 2)

Options

• A: $16.7 \mathrm{~m} / \mathrm{s}$
• B: $19.8 \mathrm{~m} / \mathrm{s}$
• C: $10.6 \mathrm{~m} / \mathrm{s}$
• D: $21.9 \mathrm{~m} / \mathrm{s}$

Question

A body is moving unidirectionally under the influence of a constant power source. Its displacement in time $\mathrm{t}$ is proportional to :

JEE Main 2024 (05 Apr Shift 2)

Options

• A: $t$
• B: $t^{3 / 2}$
• C: $t^2$
• D: $t^{2 / 3}$

Question

A circular table is rotating with an angular velocity of $\omega \mathrm{rad} / \mathrm{s}$ about its axis (see figure). There is a smooth groove along a radial direction on the table. A steel ball is gently placed at a distance of $1 \mathrm{~m}$ on the groove. All the surfaces are smooth. If the radius of the table is $3 \mathrm{~m}$, the radial velocity of the ball w.r.t. the table at the time ball leaves the table is $x \sqrt{2} \omega \mathrm{m} / \mathrm{s}$, where the value of $x$ is _____.

JEE Main 2024 (08 Apr Shift 2)

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Question

A bob of mass $m$ is suspended by a light string of length $L$. It is imparted a minimum horizontal velocity at the lowest point $A$ such that it just completes half circle reaching the top most position $B$. The ratio of kinetic energies $\frac{( K.E. {)}_A}{( K.E. {)}_B}$ is :

JEE Main 2024 (29 Jan Shift 2)

Options

• A: $3:2$
• B: $5:1$
• C: $2:5$
• D: $1:5$

Question

A body of mass $2 \mathrm{kg}$ begins to move under the action of a time dependent force given by $\overrightarrow{F}=\left(6t \hat{\mathrm{i}}+6t^2 \hat{\mathrm{j}}\right) \mathrm{N}$. The power developed by the force at the time $t$ is given by:

JEE Main 2024 (31 Jan Shift 2)

Options

• A: $\left(6t^4+9t^5\right) \mathrm{W}$
• B: $\left(3t^3+6t^5\right) \mathrm{W}$
• C: $\left(9t^5+6t^3\right) \mathrm{W}$
• D: $\left(9t^3+6t^5\right) \mathrm{W}$

Question

A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle $\left(\mathrm{\theta }\right)$ of thread deflection in the extreme position will be :

JEE Main 2024 (27 Jan Shift 2)

Options

• A: ${\tan }^{-1}\left(\sqrt{2}\right)$
• B: $2{\tan }^{-1}\left(\frac{1}{2}\right)$
• C: ${\tan }^{-1}\left(\frac{1}{2}\right)$
• D: $2{\tan }^{-1}\left(\frac{1}{\sqrt{5}}\right)$