JEE (Main) 2023
Q1
Allen
5. JEE Main PYQ
MCQ
As per given figure, a weightless pulley P is attached on a double inclined frictionless surface. The tension in the string (massless) will be (if $g = 10 \, m/s^{2}$ )
A.
$(4\sqrt{3} + 1)N$
B.
$4(\sqrt{3} + 1)N$
C.
$4(\sqrt{3} - 1)N$
D.
$(4\sqrt{3} - 1)N$
JEE (Main) 2023
Q2
Allen
5. JEE Main PYQ
MCQ
As shown in figure, a 70 kg garden roller is pushed with a force of $\vec{F} = 200\mathrm{N}$ at an angle of $30^{\circ}$ with horizontal. The normal reaction on the roller is (Given $g = 10~ms^{-2}$ )
A.
$800\sqrt{2} N$
B.
$600N$
C.
800N
D.
$200\sqrt{3} N$
JEE (Main) 2023
Q3
Allen
5. JEE Main PYQ
MCQ
As shown in the figure a block of mass 10 kg lying on a horizontal surface is pulled by a force F acting at an angle $30^{\circ}$ , with horizontal. For $\mu_{s} = 0.25$ , the block will just start to move for the value of F: [Given g = 10 ms $^{-2}$ ]
A.
$33.3N$
B.
$25.2N$
C.
$20N$
D.
$35.7N$
JEE (Main) 2023
Q4
Allen
5. JEE Main PYQ
MCQ
Consider a block kept on an inclined plane (inclined at $45^{\circ}$ ) as shown in the figure. If the force required to just push it up the incline is 2 times the force required to just prevent it from sliding down, the coefficient of friction between the block and inclined plane ( $\mu$ ) is equal to :
A.
0.33
B.
0.60
C.
0.25
D.
0.50
JEE (Advanced) 2023
Q5
Allen
7. JEE Advanced PYQ
MCQ
A particle of mass m is moving in the xy-plane such that its velocity at a point $(x, y)$ is given as $\vec{v} = \alpha(y\hat{x} + 2x\hat{y})$ , where $\alpha$ is a non-zero constant. What is the force $\vec{F}$ acting on the particle?
A.
$\vec{F} = 2m\alpha^{2}(x\hat{x} +y\hat{y})$
B.
$\vec{F} = m\alpha^{2}(y\hat{x} + 2x\hat{y})$
C.
$\vec{F} = 2m\alpha^{2}(y\hat{x} +x\hat{y})$
D.
$\vec{F} = m\alpha^{2}(x\hat{x} + 2y\hat{y})$
JEE (Main) 2022
Q6
Allen
5. JEE Main PYQ
MCQ
In the arrangement shown in figure $a_{1}, a_{2}, a_{3}$ and $a_{4}$ are the accelerations of masses $m_{1}, m_{2}, m_{3}$ and $m_{4}$ respectively. Which of the following relation is true for this arrangement?
A.
$4a_{1} + 2a_{2} + a_{3} + a_{4} = 0$
B.
$a_1 + 4a_2 + 3a_3 + a_4 = 0$
C.
$a_{1} + 4a_{2} + 3a_{3} + 2a_{4} = 0$
D.
$2a_{1} + 2a_{2} + 3a_{3} + a_{4} = 0$
JEE (Main) 2022
Q7
Allen
5. JEE Main PYQ
Numerical
A system to 10 balls each of mass 2 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 $7^{th}$ and $8^{th}$ ball is ____ N when $6^{th}$ ball just leaves the table.
Correct Answer: 36
Explanation:
Ans. (36)
$a = \frac {6 m g}{1 0 m} = \frac {6 g}{1 0} = \frac {3 g}{5}$
Taking 8, 9, 10 together
$\begin{array}{r l} & T = 3 m a \\ & = 3 m \times \frac {3 g}{5} \\ & = 3 6 N \end{array}$
$a = \frac {6 m g}{1 0 m} = \frac {6 g}{1 0} = \frac {3 g}{5}$
Taking 8, 9, 10 together
$\begin{array}{r l} & T = 3 m a \\ & = 3 m \times \frac {3 g}{5} \\ & = 3 6 N \end{array}$
JEE (Main) 2021
Q8
Allen
5. JEE Main PYQ
MCQ
A particle of mass $M$ originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation $F = F_0 \left[ 1 - \left( \frac{t - T}{T} \right)^2 \right]$
Where $F_{0}$ and T are constants. The force acts only for the time interval 2T. The velocity v of the particle after time 2T is :
A.
$2F_{0}T/M$
B.
$F_{0}T/2M$
C.
$4F_{0}T/3M$
D.
$F_{0}T/3M$
JEE (Main) 2021
Q9
Allen
5. JEE Main PYQ
MCQ
A block of mass m slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is: Given $m = 8 \, kg$ , $M = 16 \, kg$ Assume all the surfaces shown in the figure to be frictionless.
A.
$\frac{4}{3} g$
B.
$\frac{6}{5} g$
C.
$\frac{3}{5} g$
D.
$\frac{2}{3} g$
JEE (Main) 2021
Q10
Allen
5. JEE Main PYQ
Numerical
The coefficient of static friction between a wooden block of mass 0.5 kg and a vertical rough wall is 0.2. The magnitude of horizontal force that should be applied on the block to keep it adhere to the wall will be ____ N. $[g = 10 \, ms^{-2}]$
Correct Answer: 25
Explanation:
Ans. (25)
F.B.D. of the block is shown in the diagram Since block is at rest therefore
f r - m g = 0
$F - N = 0\tag{... (1}$
$f r \leq \mu N\tag{... (2}$
In limiting case
$f r = \mu N = \mu F\tag{... (3}$
Using equation (1) and (3)
$\therefore \mu F = m g$
$\Rightarrow F = \frac {0 . 5 \times 1 0}{0 . 2} = 2 5 N$
F.B.D. of the block is shown in the diagram Since block is at rest therefore
f r - m g = 0
$F - N = 0\tag{... (1}$
$f r \leq \mu N\tag{... (2}$
In limiting case
$f r = \mu N = \mu F\tag{... (3}$
Using equation (1) and (3)
$\therefore \mu F = m g$
$\Rightarrow F = \frac {0 . 5 \times 1 0}{0 . 2} = 2 5 N$
JEE (Main) 2021
Q11
Allen
5. JEE Main PYQ
Numerical
As shown in the figure, a block of mass $\sqrt{3}$ kg is kept on a horizontal rough surface of coefficient of friction $\frac{1}{3\sqrt{3}}$ . The critical force to be applied on the vertical surface as shown at an angle $60^{\circ}$ with horizontal such that it does not move, will be 3x. The value of x will be
$[g = 10m / s^2;\sin 60^\circ = \frac{\sqrt{3}}{2};\cos 60^\circ = \frac{1}{2} ]$
Correct Answer: 3
Explanation:
Ans. (3)
$F\cos 60^{\circ} = \mu N$ or $\frac{F}{2} = \frac{1}{3\sqrt{3}} N$
...(1)
and $N = \sin 60^{\circ} + \sqrt{3} g$
...(2)
From equation 1) and 2)
${\frac {F}{2}} = {\frac {1}{3 \sqrt {3}}} \left({\frac {F \sqrt {3}}{2}} + \sqrt {3} g\right)$
$\Rightarrow \quad F = g = 1 0 \mathrm{Newton} = 3 x$
So $x = \frac{10}{3} = 3.33$
$F\cos 60^{\circ} = \mu N$ or $\frac{F}{2} = \frac{1}{3\sqrt{3}} N$
...(1)
and $N = \sin 60^{\circ} + \sqrt{3} g$
...(2)
From equation 1) and 2)
${\frac {F}{2}} = {\frac {1}{3 \sqrt {3}}} \left({\frac {F \sqrt {3}}{2}} + \sqrt {3} g\right)$
$\Rightarrow \quad F = g = 1 0 \mathrm{Newton} = 3 x$
So $x = \frac{10}{3} = 3.33$
JEE (Main) 2021
Q12
Allen
5. JEE Main PYQ
Numerical
A boy of mass 4 kg is standing on a piece of wood having mass 5 kg. If the coefficient of friction between the wood and the floor is 0.5, the maximum force that the boy can exert on the rope so that the piece of wood does not move from its place is ____N. (Round off to the Nearest Integer) [Take $g = 10ms^{-2}$ ]
Correct Answer: 30
Explanation:
Ans. (30)
$N + T = 9 0$
$T = \mu N = 0.5 (9 0 - T)$
$1.5 T = 4 5$
$T = 3 0$
$N + T = 9 0$
$T = \mu N = 0.5 (9 0 - T)$
$1.5 T = 4 5$
$T = 3 0$
JEE (Main) 2021
Q13
Allen
5. JEE Main PYQ
Numerical
When a body slides down from rest along a smooth inclined plane making an angle of $30^{\circ}$ with the horizontal, it takes time T. When the same body slides down from the rest along a rough inclined plane making the same angle and through the same distance, it takes time $\alpha T$ , where is $\alpha$ constant greater than 1. The co-efficient of friction between the body and the rough plane is $\frac{1}{\sqrt{x}}\left(\frac{\alpha^{2}-1}{\alpha^{2}}\right)$ where x = .........
Correct Answer: 3
Explanation:
Ans. (3)
On smooth incline
$a = g \sin 3 0 ^ {\circ}$
By $S = ut + \frac{1}{2} at^{2}$
$S = \frac {1}{2} \frac {g}{2} T ^ {2} = \frac {g}{4} T ^ {2}\tag{... (i}$
On rough incline
$a = g \sin 3 0 ^ {\circ} - \mu g \cos 3 0 ^ {\circ}$
By $S = ut + \frac{1}{2} at^{2}$
$S = \frac {1}{4} g (1 - \sqrt {3} \mu) (\alpha T) ^ {2}\tag{... (ii}$
By (i) and (ii)
$\frac {1}{4} g T ^ {2} = \frac {1}{4} g (1 - \sqrt {3} \mu) \alpha^ {2} T ^ {2}$
$\begin{array}{r l} \Rightarrow & 1 - \sqrt {3} \mu = \frac {1}{\alpha^ {2}} \\ \Rightarrow & \mu = \left(\frac {\alpha^ {2} - 1}{\alpha^ {2}}\right) \cdot \frac {1}{\sqrt {3}} \\ \Rightarrow & x = 3. 0 0 \end{array}$
On smooth incline
$a = g \sin 3 0 ^ {\circ}$
By $S = ut + \frac{1}{2} at^{2}$
$S = \frac {1}{2} \frac {g}{2} T ^ {2} = \frac {g}{4} T ^ {2}\tag{... (i}$
On rough incline
$a = g \sin 3 0 ^ {\circ} - \mu g \cos 3 0 ^ {\circ}$
By $S = ut + \frac{1}{2} at^{2}$
$S = \frac {1}{4} g (1 - \sqrt {3} \mu) (\alpha T) ^ {2}\tag{... (ii}$
By (i) and (ii)
$\frac {1}{4} g T ^ {2} = \frac {1}{4} g (1 - \sqrt {3} \mu) \alpha^ {2} T ^ {2}$
$\begin{array}{r l} \Rightarrow & 1 - \sqrt {3} \mu = \frac {1}{\alpha^ {2}} \\ \Rightarrow & \mu = \left(\frac {\alpha^ {2} - 1}{\alpha^ {2}}\right) \cdot \frac {1}{\sqrt {3}} \\ \Rightarrow & x = 3. 0 0 \end{array}$
JEE (Main) 2021
Q14
Allen
5. JEE Main PYQ
MCQ
The boxes of masses 2 kg and 8 kg are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass 8 kg to strike the ground starting from rest. (Use g = 10 m/s $^{2}$ )
A.
0.34 s
B.
0.2 s
C.
0.25 s
D.
0.4 s
JEE (Main) 2020
Q15
Allen
5. JEE Main PYQ
Numerical
A small block starts slipping down from a point B on an inclined plane AB, which is making an angle $\theta$ with the horizontal section BC is smooth and the remaining section CA is rough with a coefficient of friction $\mu$ . It is found that the block comes to rest as it reaches the bottom (point A) of the inclined plane. If BC = 2AC, the coefficient of friction is given by $\mu = k \tan\theta$ . The value of k is ____.
Correct Answer: 3
Explanation:
Ans. (3)
Apply work energy theorem
$mg \sin \theta (AC + 2AC) - \mu mg \cos \theta AC = 0$
$\mu = 3 \tan \theta$
Apply work energy theorem
$mg \sin \theta (AC + 2AC) - \mu mg \cos \theta AC = 0$
$\mu = 3 \tan \theta$
JEE (Main) 2020
Q16
Allen
5. JEE Main PYQ
MCQ
An insect is at the bottom of a hemispherical ditch of radius 1m. It crawls up the ditch but starts slipping after it is at height h from the bottom. If the coefficient of friction between the ground and the insect is 0.75, then h is: $(g = 10 \, ms^{-2})$
A.
0.80 m
B.
0.60 m
C.
0.45 m
D.
0.20 m
JEE (Main) 2020
Q17
Allen
5. JEE Main PYQ
MCQ
A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force F is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of $45^{\circ}$ with the vertical. Then F equals: (Take $g = 10 \, ms^{-2}$ and the rope to be massless)
A.
100 N
B.
90 N
C.
75 N
D.
70 N
JEE (Main) 2019
Q18
Allen
5. JEE Main PYQ
MCQ
Two blocks A and B of masses $m_{A} = 1 \, kg$ and $m_{B} = 3 \, kg$ are kept on the table as shown in figure. The coefficient of friction between A and B is 0.2 and between B and the surface of the table is also 0.2. The maximum force F that can be applied on B horizontally, so that the block A does not slide over the block B is: (Take $g = 10 \, m/s^{2}$ )
A.
$16N$
B.
$40N$
C.
$12N$
D.
$8N$
JEE (Main) 2019
Q19
Allen
5. JEE Main PYQ
MCQ
A ball is thrown upward with an initial velocity $V_{0}$ from the surface of the earth. The motion of the ball is affected by a drag force equal to $m\gamma v^{2}$ (where m is mass of the ball, $\upsilon$ is its instantaneous velocity and $\gamma$ is a constant). Time taken by the ball to rise to its zenith is
A.
$\frac{1}{\sqrt{\gamma g}}\sin^{-1}\left(\sqrt{\frac{\gamma}{g}}V_{0}\right)$
B.
$\frac{1}{\sqrt{\gamma g}}\tan^{-1}\left(\sqrt{\frac{\gamma}{g}}V_{0}\right)$
C.
$\frac{1}{\sqrt{2\gamma g}}\tan^{-1}\left(\sqrt{\frac{2\gamma}{g}}V_{0}\right)$
D.
$\frac{1}{\sqrt{\gamma g}}\ln\left(1+\sqrt{\frac{\gamma}{g}}V_{0}\right)$
JEE (Main) 2019
Q20
Allen
5. JEE Main PYQ
MCQ
A spring whose unstretched length is $l$ has a force constant $k$ . The spring is cut into two pieces of unstretched lengths $l_{1}$ and $l_{2}$ where, $l_{1} = nl_{2}$ and $n$ is an integer. The ratio $k_{1}/k_{2}$ of the corresponding force constants, $k_{1}$ and $k_{2}$ will be :
A.
$\frac{1}{n^2}$
B.
$n^2$
C.
$\frac{1}{n}$
D.
$n$
JEE (Main) 2018
Q21
Allen
5. JEE Main PYQ
MCQ
Two masses $m_{1} = 5 \, kg$ and $m_{2} = 10 \, kg$ , connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is 0.15. The minimum weight m that should be put on top of $m_{2}$ to stop the motion is :-
A.
27.3 kg
B.
43.3 kg
C.
10.3 kg
D.
18.3 kg
JEE (Main) 2016
Q22
Allen
5. JEE Main PYQ
MCQ
A rocket is fired vertically from the earth with an acceleration of $2g$ , where $g$ is the gravitational acceleration. On an inclined plane inside the rocket, making an angle $\theta$ with the horizontal, a point object of mass $m$ is kept. The minimum coefficient of friction $\mu_{\mathrm{min}}$ between the mass and the inclined surface such that the mass does not move is:
A.
$2\tan \theta$
B.
$3\tan \theta$
C.
$\tan \theta$
D.
$\tan 2\theta$
JEE (Main) 2015
Q23
Allen
5. JEE Main PYQ
MCQ
Given in the figure are two blocks A and B of weight 20N and 100N, respectively. These are being pressed against a wall by a force F as shown. If the coefficient of friction between the blocks is 0.1 and between block B and the wall is 0.15, the frictional force applied by the wall on block B is :-
A.
120 N
B.
150 N
C.
100 N
D.
80 N
JEE (Main) 2014
Q24
Allen
5. JEE Main PYQ
MCQ
A block of mass m is placed on a surface with a vertical cross section given by $y=\frac{x^{3}}{6}$ . If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is :-
A.
$\frac{1}{3}m$
B.
$\frac{1}{2}m$
C.
$\frac{1}{6}m$
D.
$\frac{2}{3}m$
JEE (Advanced) 2014
Q25
Allen
7. JEE Advanced PYQ
Match the Columns
A block of mass $m_{1} = 1kg$ another mass $m_{2} = 2kg$ , are placed together (see figure) on an inclined plane with angle of inclination $\theta$ . Various values of $\theta$ are given in Column-I. The coefficient of friction between the block $m_{1}$ and the plane is always zero. The coefficient of static and dynamic friction between the block $m_{2}$ and the plane are equal to $\mu = 0.3$ . In Column-II expressions for the friction on block $m_{2}$ are given. Match the correct expression of the friction in Column-II with the angles given in Column-I and choose the correct option. The acceleration due to gravity is denoted by g.
[Useful information : tan (5.5°) ≈ 0.1 ; tan(11.5°) ≈ 0.2 ; tan (16.5°) ≈ 0.3]
[Useful information : tan (5.5°) ≈ 0.1 ; tan(11.5°) ≈ 0.2 ; tan (16.5°) ≈ 0.3]
| Column-I | Column-II | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
A.
I-P, II-P, III-P, IV-R
B.
I-Q, II-Q, III-Q, IV-R
C.
I-Q, II-Q, III-Q, IV-S
D.
I-Q, II-Q, III-R, IV-R
