iCON Education

JEE (Main) 2022 Q51 Allen JEE Main PYQ Numerical

iCON Education HYD, 79930 92826, 73309 72826

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.

JEE (Main) June 2022 Q52 Errorless Critical Thinking MCQ

iCON Education HYD, 79930 92826, 73309 72826

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) June 2022 Q53 Errorless Critical Thinking MCQ

iCON Education HYD, 79930 92826, 73309 72826

A block of mass M placed inside a box descends vertically with acceleration ‘a’. The block exerts a force equal to one-fourth of its weight on the floor of the box. The value of ‘a’ will be

A.

$\frac{g}{4}$

B.

$\frac{g}{2}$

C.

$\frac{3g}{4}$

D.

g

JEE (Main) June 2022 Q54 Errorless Critical Thinking MCQ

iCON Education HYD, 79930 92826, 73309 72826

A block of mass 2 kg moving on a horizontal surface with speed of $4 \, ms^{-1}$ enters a rough surface ranging from x = 0.5 m to x = 1.5 m. The retarding force in this range of rough surface is related to distance by F = -kx where $k = 12 \, Nm^{-1}$ . The speed of the block as it just crosses the rough surface will be

A.

Zero

B.

$1.5 \, ms^{-1}$

C.

$2.0 \, ms^{-1}$

D.

$2.5 \, ms^{-1}$

JEE (Main) June 2022 Q55 Errorless Critical Thinking MCQ

iCON Education HYD, 79930 92826, 73309 72826

A $\sqrt{34} m$ long ladder weighing $10kg$ leans on a frictionless wall. Its feet rest on the floor $3m$ away from the wall as shown in the figure. If $F_{f}$ and $F_{w}$ are the reaction forces of the floor and the wall, then ratio of $F_{w}/F_{f}$ will be (Use $g=10m/s^{2}$ )

A.

$\frac {6}{\sqrt {1 1 0}}$

B.

$\frac {3}{\sqrt {1 1 3}}$

C.

$\frac {3}{\sqrt {1 0 9}}$

D.

$\frac {2}{\sqrt {1 0 9}}$

JEE (Main) June 2022 Q56 Errorless Critical Thinking MCQ

iCON Education HYD, 79930 92826, 73309 72826

A body of mass M at rest explodes into three pieces, in the ratio of masses 1:1:2. Two smaller pieces fly off perpendicular to each other with velocities of $30 \, ms^{-1}$ and $40 \, ms^{-1}$ respectively. The velocity of the third piece will be

A.

$15 \, ms^{-1}$

B.

$25 \, ms^{-1}$

C.

$35 \, ms^{-1}$

D.

$50 \, ms^{-1}$

JEE (Main) June 2022 Q57 Errorless Critical Thinking MCQ

iCON Education HYD, 79930 92826, 73309 72826

A person is standing in an elevator. In which situation, he experiences weight loss

A.

When the elevator moves upward with constant acceleration

B.

When the elevator moves downward with constant acceleration

C.

When the elevator moves upward with uniform velocity

D.

When the elevator moves downward with uniform velocity

JEE (Main) June 2022 Q58 Errorless Critical Thinking MCQ

iCON Education HYD, 79930 92826, 73309 72826

A block of metal weighing 2 kg is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of $1 \, kgs^{-1}$ and at a speed of $10 \, ms^{-1}$ . Then, the initial acceleration of the block, in $ms^{-2}$ , will be

Plane

A.

3

B.

6

C.

5

D.

4

JEE (Main) July 2022 Q59 Errorless Critical Thinking MCQ

iCON Education HYD, 79930 92826, 73309 72826

Two billiard balls of mass 0.05 kg each moving in opposite directions with $10 \, ms^{-1}$ collide and rebound with the same speed. If the time duration of contact is t = 0.005s, then what is the force exerted on the ball due to each other

A.

100 N

B.

200 N

C.

300 N

D.

400 N

JEE (Main) July 2022 Q60 Errorless Critical Thinking MCQ

iCON Education HYD, 79930 92826, 73309 72826

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

A.

$\sqrt{2} N,45^{\circ}$

B.

$\sqrt{2} N,135^{\circ}$

C.

$\frac{2}{\sqrt{3}} N,30^{\circ}$

D.

$2N,45^{\circ}$

JEE (Main) July 2022 Q61 Errorless Critical Thinking MCQ

iCON Education HYD, 79930 92826, 73309 72826

In two different experiments, an object of mass 5 kg moving with a speed of $25 \, ms^{-1}$ hits two different walls and comes to rest within (i) 3 second, (ii) 5 seconds, respectively. Choose the correct option out of the following

A.

Impulse and average force acting on the object will be same for both the cases

B.

Impulse will be same for both the cases but the average force will be different

C.

Average force will be same for both the cases but the impulse will be different

D.

Average force and impulse will be different for both the cases

JEE (Main) July 2022 Q62 Errorless Critical Thinking MCQ

iCON Education HYD, 79930 92826, 73309 72826

A balloon has mass of 10 g in air. The air escapes from the balloon at a uniform rate with velocity 4.5 cm/s. If the balloon shrinks in 5 s completely. Then, the average force acting on that balloon will be (in dyne)

A.

3

B.

9

C.

12

D.

18

JEE (Main) July 2022 Q63 Errorless Critical Thinking MCQ

iCON Education HYD, 79930 92826, 73309 72826

The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at $(4 + x)$ cm inside the block. The value of x is

A.

2.0

B.

1.0

C.

0.5

D.

1.5

JEE (Main) July 2022 Q64 Errorless Critical Thinking MCQ

iCON Education HYD, 79930 92826, 73309 72826

Two bodies of masses $m_{1}=5kg$ and $m_{2}=3kg$ are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass $m_{1}$ will be [Take $g=10ms^{-2}$ ]

A.

30 N

B.

40 N

C.

50 N

D.

60 N

JEE (Main) July 2022 Q65 Errorless Critical Thinking MCQ

iCON Education HYD, 79930 92826, 73309 72826

Three masses $M = 100 \, \text{kg}$ , $m_1 = 10 \, \text{kg}$ and $m_2 = 20 \, \text{kg}$ 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 $2 \, \text{ms}^{-2}$ . The value of $F$ is (Take $g = 10 \, \text{ms}^{-2}$ )

A.

3360 N

B.

3380 N

C.

3120 N

D.

3240 N

JEE (Main) July 2022 Q66 Errorless Critical Thinking MCQ

iCON Education HYD, 79930 92826, 73309 72826

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

A.

T = 700N while climbing upward

B.

T = 350N while going downward

C.

Rope will break while climbing upward

D.

Rope will break while climbing downward

JEE (Main) July 2022 Q67 Errorless Critical Thinking MCQ

iCON Education HYD, 79930 92826, 73309 72826

A ball of mass 0.15 kg hits the wall with its initial speed of $12 \, ms^{-1}$ and bounces back without changing its initial speed. If the force applied by the wall on the ball during the contact is 100 N. Calculate the time duration of the contact of ball with the wall

A.

0.018 s

B.

0.036 s

C.

0.009 s

D.

0.072 s

JEE (Main) July 2022 Q68 Errorless Critical Thinking MCQ

iCON Education HYD, 79930 92826, 73309 72826

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 ____

A.

6

B.

2

C.

1.5

D.

4

JEE (Main) July 2022 Q69 Errorless Critical Thinking MCQ

iCON Education HYD, 79930 92826, 73309 72826

Two masses $M_{1}$ and $M_{2}$ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass $M_{2}$ is twice that of $M_{1}$ , the acceleration of the system is $a_{1}$ . When the mass $M_{2}$ is thrice that of $M_{1}$ , the acceleration of the system is $a_{2}$ . The ratio $\frac{a_{1}}{a_{2}}$ will be

A.

1/3

B.

2/3

C.

3/2

D.

1/2

JEE (Main) July 2022 Q70 Errorless Critical Thinking MCQ

iCON Education HYD, 79930 92826, 73309 72826

A block of mass M slides down on a rough inclined plane with constant velocity. The angle made by the incline plane with horizontal is $\theta$ . The magnitude of the contact force will be

A.

Mg

B.

Mg cos $\theta$

C.

$\sqrt{Mg\sin\theta+Mg\cos\theta}$

D.

$Mg\sin\theta\sqrt{1+\mu}$

JEE (Main) June 2022, Jan. 2023, April 2024 Q71 Errorless Critical Thinking MCQ

iCON Education HYD, 79930 92826, 73309 72826

A block of $\sqrt{3}$ kg is attached to a string whose other end is attached to the wall. An unknown force F is applied so that the string makes an angle of $30^{\circ}$ with the wall. The tension T is (Given $g = 10 ms^{-2}$ )

A.

20N

B.

25N

C.

10N

D.

15N

JEE (Advanced) 2022 Q72 Errorless JEE Section Numerical

iCON Education HYD, 79930 92826, 73309 72826

A particle of mass 1 kg is subjected to a force which depends on the position as $\vec{F} = -k(x\hat{i} + y\hat{j})kgms^{-2}$ with $k = 1kgs^{-2}$ . At time $t = 0$ , the particle's position $\vec{r} = \left(\frac{1}{\sqrt{2}}\hat{i} + \sqrt{2}\hat{j}\right)m$ and its velocity $\vec{v} = \left(-\sqrt{2}\hat{i} + \sqrt{2}\hat{j} + \frac{2}{\pi}\hat{k}\right)ms^{-1}$ . Let $v_x$ and $v_y$ denote the $x$ and the $y$ components of the particle's velocity respectively. Ignore gravity when $z = 0.5m$ , the value of $(xv_y - yv_x)$ is ____ $m^2 s^{-1}$

Correct Answer: 3

Explanation:

$F_{x} = -x = ma_{x}$
So $a_{x} = \frac{d^{2}x}{dt^{2}} = -x$
$\Rightarrow x = A _ {x} \sin (\omega t + \phi_ {x}) \quad (\omega = 1 r a d / s)$
and $v_{x} = A_{x}\omega \cos (\omega t + \phi_{x})$
at $t = 0$ , $x = \frac{1}{\sqrt{2}} m$ and $v_{x} = -\sqrt{2} m / s$
$\text { So } A _ {x} \sin \phi_ {x} = \frac {1}{\sqrt {2}} \text { and } A _ {x} \cos \phi_ {x} = - \sqrt {2}$
$\Rightarrow \tan \phi_ {x} = - \frac {1}{2}\tag{... (i}$
and $A_{x}=\sqrt{\frac{5}{2}}m$
... (ii)
Similarly, $F_{y} = -y = ma_{y}$
$\Rightarrow \frac {d ^ {2} y}{d t ^ {2}} = - y$
$\mathrm{So}, y = A _ {y} \sin (\omega t + \phi_ {y}) \quad (\omega = 1 r a d / s)$
and $v_{y} = A_{y}\omega \cos (\omega t + \phi_{y})$
at $t = 0, y = \sqrt{2} m$ and $v_{y} = \sqrt{2} m / s$
So $A_{y}\sin \phi_{y} = \sqrt{2}$ and $A_{y}\cos \phi_{y} = \sqrt{2}$
$\Rightarrow \phi = \frac {\pi}{4}\tag{... (iii}$
and $A_{y} = 2$
$\begin{array}{r l} & {\mathrm{So}, (x v _ {y} - y v _ {x}) = \sqrt {\frac {5}{2}} \sin (\omega t + \phi_ {x}) \times 2 \cos (\omega t + \phi_ {y}) -} \\ & {\qquad \qquad \qquad \qquad \qquad 2 \sin (\omega t + \phi_ {y}) \times \sqrt {\frac {5}{2}} \cos (\omega t + \phi_ {x})} \\ & {\Rightarrow x v _ {y} - y v _ {x} = \sqrt {\frac {5}{2}} \times 2 [ \sin (\omega t + \phi_ {x}) \cos (\omega t + \phi_ {y}) -} \\ & {\qquad \qquad \qquad \qquad \qquad \sin (\omega t + \phi_ {y}) \cos (\omega t + \phi_ {x}) ]} \\ & {\Rightarrow x v _ {y} - y v _ {x} = \sqrt {1 0} \sin (\phi_ {x} - \phi_ {y})} \\ & {\Rightarrow x v _ {y} - y v _ {x} = \sqrt {1 0} [ \sin \phi_ {x} \cos \phi_ {y} - \cos \phi_ {x} \sin \phi_ {y} ]} \\ & {\Rightarrow x v _ {y} - y v _ {x} = \sqrt {1 0} \left[ \frac {1}{\sqrt {5}} \times \frac {1}{\sqrt {2}} - \left(- \frac {2}{\sqrt {5}}\right) \times \frac {1}{\sqrt {2}} \right]} \\ & {\Rightarrow x v _ {y} - y v _ {x} = 3.} \end{array}\tag{... (iv}$

JEE (Main) June 2022 Q73 Errorless Critical Thinking-friction MCQ

iCON Education HYD, 79930 92826, 73309 72826

A block of mass 10 kg starts sliding on a surface with an initial velocity of $9.8 \, ms^{-1}$ . The coefficient of friction between the surface and block is 0.5. The distance covered by the block before coming to rest is [use $g = 9.8 \, ms^{-2}$ ]

A.

4.9 m

B.

9.8 m

C.

12.5 m

D.

19.6 m

JEE (Main) June 2022 Q74 Errorless Critical Thinking-friction MCQ

iCON Education HYD, 79930 92826, 73309 72826

A block of mass 40 kg slides over a surface, when a mass of 4 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 $g = 10 ms^{-2}$ )

A.

$1ms^{-2}$

B.

$1 / 5ms^{-2}$

C.

$4 / 5ms^{-2}$

D.

$8 / 11ms^{-2}$

JEE (Main) July 2022 Q75 Errorless Critical Thinking-friction MCQ

iCON Education HYD, 79930 92826, 73309 72826

A bag is gently dropped on a conveyor belt moving at a speed of 2m/s. The coefficient of friction between the conveyor belt and bag is 0.4. Initially, the bag slips on the belt before it stops due to friction. The distance travelled by the bag on the belt during slipping motion is [Take $g = 10m/s^{2}$ ]

A.

2 m

B.

0.5 m

C.

3.2 m

D.

0.8 m

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