Question

A block of mass $m$ slides along a floor while a force of magnitude $F$ is applied to it at an angle $\theta$ as shown in figure. The coefficient of kinetic friction is ${\mu }_K$. Then, the block's acceleration $a$ is given by : ($g$ is acceleration due to gravity)

JEE Main 2021 (16 Mar Shift 1)

Options

• A: $-\frac{F}{m}\cos \theta -{\mu }_K\left(g-\frac{F}{m}\sin \theta \right)$
• B: $\frac{F}{m}\cos \theta -{\mu }_K\left(g-\frac{F}{m}\sin \theta \right)$
• C: $\frac{F}{m}\cos \theta -{\mu }_K\left(g+\frac{F}{m}\sin \theta \right)$
• D: $\frac{F}{m}\cos \theta +{\mu }_K\left(g-\frac{F}{m}\sin \theta \right)$

Question

A steel block of $10 \mathrm{kg}$ rests on a horizontal floor as shown. When three iron cylinders are placed on it as shown, the block and cylinders go down with an acceleration $0.2 \mathrm{m} {\mathrm{s}}^{-2}.$ The normal reaction $R^{\text{'}}$ by the floor if mass of the iron cylinders are equal and of $20 \mathrm{kg}$ each is $\left(\text{in} \mathrm{N}\right)$,

[Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$ and $\left.{\mu }_{\mathrm{s}}=0.2\right]$

JEE Main 2021 (20 Jul Shift 1)

Options

• A: $716$
• B: $686$
• C: $714$
• D: $684$

Question

Two blocks ($m=0.5 \mathrm{kg}$ and $M=4.5 \mathrm{kg}$) are arranged on a horizontal frictionless table as shown in the figure. The coefficient of static friction between the two blocks is $\frac{3}{7}.$ Then the maximum horizontal force that can be applied on the larger block so that the blocks move together is $N.$ (Round off to the Nearest Integer) [Take $g$ as $9.8 \mathrm{m} {\mathrm{s}}^{-2}$]

JEE Main 2021 (17 Mar Shift 1)

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Question

For a free body diagram shown in the figure, the four forces are applied in the '$x$' and '$y$' directions. What additional force must be applied and at what angle with positive $x$-axis so that the net acceleration of body is zero?

JEE Main 2022 (25 Jul Shift 2)

Options

• A: $\sqrt{2} \mathrm{N},45°$
• B: $\sqrt{2} \mathrm{N},135°$
• C: $\frac{2}{\sqrt{3}} \mathrm{N},30°$
• D: $2 \mathrm{N},45°$

Question

Three masses $M=100 \mathrm{kg},{ m}_1=10 \mathrm{kg}$ and $m_2=20 \mathrm{kg}$ are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. A force $F$ is applied on the system so that the mass $m_2$ moves upward with an acceleration of $2{ \mathrm{ms}}^{-2}$. The value of $F$ is

(Take $g=10{ \mathrm{ms}}^{-2}$)

JEE Main 2022 (26 Jul Shift 1)

Options

• A: $3360 \mathrm{N}$
• B: $3380 \mathrm{N}$
• C: $3120\mathrm{N}$
• D: $3240\mathrm{N}$

Question

A monkey of mass $50 \mathrm{kg}$ climbs on a rope which can withstand the tension $\left(T\right)$ of $350 \mathrm{N}$. If monkey initially climbs down with an acceleration of $4 \mathrm{m} {\mathrm{s}}^{-2}$ and then climbs up with an acceleration of $5 \mathrm{m} {\mathrm{s}}^{-2}$. Choose the correct option $\left(\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

JEE Main 2022 (26 Jul Shift 1)

Options

• A: $T=700 \mathrm{N}$ while climbing upward
• B: $T=350 \mathrm{N}$ while going downward
• C: Rope will break while climbing upward
• D: Rope will break while going downward

Question

A block $A$ takes $2 \mathrm{s}$ to slide down a frictionless incline of $30°$ and length $l$, kept inside a lift going up with uniform velocity $v$. If the incline is changed to $45°$, the time taken by the block, to slide down the incline, will be approximately:

JEE Main 2022 (27 Jul Shift 2)

Options

• A: $2.66 \mathrm{s}$
• B: $0.83 \mathrm{s}$
• C: $1.68 \mathrm{s}$
• D: $0.70 \mathrm{s}$

Question

A uniform metal chain of mass $m$ and length $L$ passes over a massless and frictionless pulley. It is released from rest with a part of its length $l$ is hanging on one side and rest of its length $L-l$  is hanging on the other side of the pulley. At a certain point of time, when $l=\frac{L}{x}$, the acceleration of the chain is $\frac{g}{2}$. The value of $x$ is _____.

JEE Main 2022 (28 Jul Shift 2)

Options

• A: $6$
• B: $2$
• C: $1.5$
• D: $4$

Question

A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass $m$ moves against the wall with a speed $v$. Which of the following curve represents the correct relation between the normal reaction on the block by the wall $\left(N\right)$ and speed of the block $\left(v\right)$?

JEE Main 2022 (29 Jul Shift 1)

Options

• A:
• B:
• C:
• D:

Question

A block of mass $40 \mathrm{kg}$ slides over a surface, when a mass of $4 \mathrm{kg}$ is suspended through an inextensible massless string passing over frictionless pulley as shown below.
The coefficient of kinetic friction between the surface and block is $0.02$. The acceleration of block is: (Given $g=10{ \mathrm{m} \mathrm{s}}^{-2}$.)

JEE Main 2022 (29 Jun Shift 2)

Options

• A: $\frac{8}{11} \mathrm{m} {\mathrm{s}}^{-2}$
• B: $1 \mathrm{m} {\mathrm{s}}^{-2}$
• C: $\frac{1}{5} \mathrm{m} {\mathrm{s}}^{-2}$
• D: $\frac{4}{5} \mathrm{m} {\mathrm{s}}^{-2}$

Question

Four forces are acting at a point $P$ in equilibrium as shown in figure. The ratio of force $F_1$ to $F_2$ is $1:x$ where $x=$_____ .

JEE Main 2022 (25 Jul Shift 1)

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Question

A system to $10$ balls each of mass $2 \mathrm{kg}$ are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the $7^{\mathrm{th} }$ and $8^{\mathrm{th} }$ ball is _____  $\mathrm{N}$ when $6^{\mathrm{th} }$ ball just leaves the table.

JEE Main 2022 (26 Jun Shift 2)

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Question

A block of mass $5 \mathrm{kg}$ is placed at rest on a table of rough surface. Now, if a force of $30 \mathrm{N}$ is applied in the direction parallel to surface of the table, the block slides through a distance of $50 \mathrm{m}$ in an interval of time $10 \mathrm{s}$. Coefficient of kinetic friction is (given, $g = 10 \mathrm{m} {\mathrm{s}}^{–2}$ ):

JEE Main 2023 (01 Feb Shift 1)

Options

• A: $0.60$
• B: $0.75$
• C: $0.50$
• D: $0.25$

Question

The time taken by an object to slide down $45°$ rough inclined plane is $n$ times as it takes to slide down a perfectly smooth $45°$ incline plane. The coefficient of kinetic friction between the object and the incline plane is:

JEE Main 2023 (29 Jan Shift 2)

Options

• A: $\sqrt{\frac{1}{1-n^2}}$
• B: $\sqrt{1-\frac{1}{n^2}}$
• C: $1+\frac{1}{n^2}$
• D: $1-\frac{1}{n^2}$

Question

The figure represents the momentum time $(p-t)$ curve for a particle moving along an axis under the influence of the force. Identify the regions on the graph where the magnitude of the force is maximum and minimum respectively ?

If $\left(t_3-t_2\right)<t_1$

JEE Main 2023 (30 Jan Shift 1)

Options

• A: c and a
• B: b and c
• C: c and b
• D: a and b

Question

A coin placed on a rotating table just slips when it is placed at a distance of $1 \mathrm{cm}$ from the centre. If the angular velocity of the table is halved, it will just slip when placed at a distance of _____ from the centre:

JEE Main 2023 (11 Apr Shift 1)

Options

• A: $8 \mathrm{cm}$
• B: $4 \mathrm{cm}$
• C: $1 \mathrm{cm}$
• D: $2 \mathrm{cm}$

Question

A wooden block, initially at rest on the ground, is pushed by a force which increases linearly with time $t$. Which of the following curve best describes acceleration of the block with time:

JEE Main 2024 (04 Apr Shift 1)

Options

• A:
  
• B:
  
• C:
  
• D:
  

Question

Three blocks $M_1, M_2, M_3$ having masses $4 \mathrm{~kg}, 6 \mathrm{~kg}$ and $10 \mathrm{~kg}$ respectively are hanging from a smooth pully using rope 1,2 and 3 as shown in figure. The tension in the rope $1, T_1$ when they are moving upward with acceleration of $2 \mathrm{~ms}^{-2}$ is _____$\mathrm{N}\left(\right.$ if $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ ).

JEE Main 2024 (05 Apr Shift 1)

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Question

A light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (where $m_2>m_1$ ). If the acceleration of the system is $\frac{g}{\sqrt{2}}$, then the ratio of the masses $\frac{m_1}{m_2}$ is:

JEE Main 2024 (06 Apr Shift 1)

Options

• A: $\frac{1+\sqrt{5}}{\sqrt{5}-1}$
• B: $\frac{\sqrt{2}-1}{\sqrt{2}+1}$
• C: $\frac{1+\sqrt{5}}{\sqrt{2}-1}$
• D: $\frac{\sqrt{3}+1}{\sqrt{2}-1}$

Question

A given object takes $\mathrm{n}$ times the time to slide down $45^{\circ}$ rough inclined plane as it takes the time to slide down an identical perfectly smooth $45^{\circ}$ inclined plane. The coefficient of kinetic friction between the object and the surface of inclined plane is :

JEE Main 2024 (08 Apr Shift 2)

Options

• A: $\sqrt{1-\frac{1}{n^2}}$
• B: $1-n^2$
• C: $1-\frac{1}{n^2}$
• D: $\sqrt{1-n^2}$

Question

A stone of mass $900 \mathrm{g}$ is tied to a string and moved in a vertical circle of radius $1 \mathrm{m}$ making $10 \mathrm{rpm}$. The tension in the string, when the stone is at the lowest point is (if ${\pi }^2=9.8$ and $g=9.8 \mathrm{m} {\mathrm{s}}^{-2}$)

JEE Main 2024 (29 Jan Shift 2)

Options

• A: $97 \mathrm{N}$
• B: $9.8 \mathrm{N}$
• C: $8.82 \mathrm{N}$
• D: $17.8 \mathrm{N}$

Question

In the given arrangement of a doubly inclined plane two blocks of masses $M$ and $m$ are placed. The blocks are connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface of the plane and the blocks is $0.25$. The value of $m$, for which $M=10 \mathrm{kg}$ will move down with an acceleration of $2 \mathrm{m} {\mathrm{s}}^{-2}$, is: (take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$ and $\tan 37°=\frac{3}{4}$)

JEE Main 2024 (31 Jan Shift 1)

Options

• A: $9 \mathrm{kg}$
• B: $4.5 \mathrm{kg}$
• C: $6.5 \mathrm{kg}$
• D: $2.25 \mathrm{kg}$

Question

A train is moving with a speed of $12 \mathrm{m} {\mathrm{s}}^{-1}$ on rails which are $1.5 \mathrm{m}$ apart. To negotiate a curve radius $400 \mathrm{m}$, the height by which the outer rail should be raised with respect to the inner rail is (Given, $g=$ $10 \mathrm{m} {\mathrm{s}}^{-2}$):

JEE Main 2024 (27 Jan Shift 1)

Options

• A: $6.0 \mathrm{cm}$
• B: $5.4 \mathrm{cm}$
• C: $4.8 \mathrm{cm}$
• D: $4.2 \mathrm{cm}$

Question

A block of mass $5 \mathrm{kg}$ is placed on a rough inclined surface as shown in the figure. If ${\overrightarrow{F}}_1$ is the force required to just move the block up the inclined plane and ${\overrightarrow{F}}_2$ is the force required to just prevent the block from sliding down, then the value of $\left|{\overrightarrow{F}}_1\right|-\left|{\overrightarrow{F}}_2\right|$ is: [Use $g=10 \mathrm{m} {\mathrm{s}}^{-2}$]

JEE Main 2024 (31 Jan Shift 2)

Options

• A: $25\sqrt{3} \mathrm{N}$
• B: $5\sqrt{3} \mathrm{N}$
• C: $\frac{5\sqrt{3}}{2} \mathrm{N}$
• D: $10 \mathrm{N}$