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255 Questions Start Errorless Test
All Exams Allen Advance Errorless
JEE (Main) Jan. 2023 Q26 Errorless 7. Critical Thinking MCQ
Force acts for 20 s on a body of mass 20 kg, starting from rest, after which the force ceases and then body describes 50 m in the next 10 s. The value of force will be
A.
40 N
B.
5 N
C.
20 N
D.
10 N
JEE (Main) Jan. 2023 Q27 Errorless 7. Critical Thinking MCQ
A machine gun of mass 10 kg fires 20 g bullets at the rate of 180 bullets per minute with a speed of $100 \, ms^{-1}$ each. The recoil velocity of the gun is
A.
0.02 m/s
B.
2.5 m/s
C.
1.5 m/s
D.
0.6 m/s
JEE (Main) Jan. 2023 Q28 Errorless 7. Critical Thinking MCQ
As shown in figure, a 70 kg garden roller is pushed with a force of $\vec{F} = 200 N$ 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) Jan. 2023 Q29 Errorless 7. Critical Thinking MCQ
100 balls each of mass m moving with speed v simultaneously strike a wall normally and reflected back with same speed, in time t s. The total force exerted by the balls on the wall is
A.
$\frac{100\,mv}{t}$
B.
$\frac{200\,mv}{t}$
C.
200 mvt
D.
$\frac{mv}{100\,t}$
JEE (Main) Jan. 2023 Q30 Errorless 7. Critical Thinking MCQ
A stone of mass 1kg is tied to end of a massless string of length 1m. If the breaking tension of the string is 400N, then maximum linear velocity, the stone can have without breaking the string, while rotating in horizontal plane, is
A.
$20ms^{-1}$
B.
$40ms^{-1}$
C.
$400ms^{-1}$
D.
$10ms^{-1}$
JEE (Main) April 2023 Q31 Errorless 7. Critical Thinking MCQ
Three force $F_{1}=10N, F_{2}=8N, F_{3}=6N$ are acting on a particle of mass 5 kg. The forces $F_{2}$ and $F_{3}$ are applied perpendicular so that particle remains at rest. If the force $F_{1}$ is removed, then the acceleration of the particle is
A.
$2\ ms^{-2}$
B.
$0.5\ ms^{-2}$
C.
$4.8\ ms^{-2}$
D.
$7\ ms^{-2}$
JEE (Main) April 2023 Q32 Errorless 7. Critical Thinking MCQ
At any instant the velocity of a particle of mass 500 g is $(2t\hat{i}+3t^{2}\hat{j})ms^{-1}$ . If the force acting on the particle at t=1s is $(\hat{i}+x\hat{j})N$ . Then the value of x will be
A.
3
B.
4
C.
6
D.
2
JEE (Main) April 2023 Q33 Errorless 7. Critical Thinking MCQ
A body of mass 500 g moves along x-axis such that it's velocity varies with displacement x according to the relation $v = 10\sqrt{x} \, m/s$ , the force acting on the body is
A.
166 N
B.
25 N
C.
125 N
D.
5 N
JEE (Main) April 2023 Q34 Errorless 7. Critical Thinking MCQ
An average force of 125 N is applied on a machine gun firing bullets each of mass 10 g at the speed of 250 m/s to keep it in position. The number of bullets fired per second by the machine gun is
A.
5
B.
50
C.
100
D.
25
JEE (Main) April 2023 Q35 Errorless 7. Critical Thinking MCQ
A bullet 10 g leaves the barrel of gun with a velocity of 600 m/s. If the barrel of gun is 50 cm long and mass of gun is 3 kg, then value of impulse supplied to the gun will be
A.
12 Ns
B.
6 Ns
C.
36 Ns
D.
3 Ns
JEE (Advanced) 2023 Q36 Errorless 7. Critical Thinking 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) Jan. 2023 Q37 Errorless 8. Graphical Questions MCQ
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 $(t_{3}-t_{2})
A.
c and a
B.
b and c
C.
c and b
D.
a and b
JEE (Main) Jan. 2023 Q38 Errorless 14. Critical Thinking-friction 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 (Main) Jan. 2023 Q39 Errorless 14. Critical Thinking-friction MCQ
A block of mass m slides down the plane inclined at angle $30^{\circ}$ with an acceleration $\frac{g}{4}$ . The value of coefficient of kinetic friction will be
A.
$\frac{2\sqrt{3}+1}{2}$
B.
$\frac{1}{2\sqrt{3}}$
C.
$\frac{\sqrt{3}}{2}$
D.
$\frac{2\sqrt{3}-1}{2}$
JEE (Main) Jan. 2023 Q40 Errorless 14. Critical Thinking-friction MCQ
A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of car will be, if friction between tyres and road is 0.34 [Take $g = 10 ms^{-2}$ ]
A.
$3.4 ms^{-1}$
B.
$22.4 ms^{-1}$
C.
$13 ms^{-1}$
D.
$17 ms^{-1}$
JEE (Main) Jan. 2023 Q41 Errorless 14. Critical Thinking-friction MCQ
The time taken by an object to slide down $45^{\circ}$ rough inclined plane is n times as it takes to slide down a perfectly smooth $45^{\circ}$ incline place. The coefficient of kinetic friction between the object and the incline plane is
A.
$\sqrt{\frac{1}{1-n^{2}}}$
B.
$\sqrt{1-\frac{1}{n^{2}}}$
C.
$1+\frac{1}{n^{2}}$
D.
$1-\frac{1}{n^{2}}$
JEE (Main) Jan. 2023 Q42 Errorless 14. Critical Thinking-friction MCQ
A body of mass 10kg is moving with an initial speed of 20m/s. The body stops after 5s due to friction between body and the floor. The value of the coefficient of friction is (Take acceleration due to gravity $g = 10ms^{-2}$ )
A.
0.2
B.
0.3
C.
0.5
D.
0.4
JEE (Main) Jan. 2023 Q43 Errorless 14. Critical Thinking-friction MCQ
A block of mass $5kg$ is placed at rest on a table of rough surface. Now, if a force of $30N$ is applied in the direction parallel to surface of the table, the block slides through a distance of $50m$ in an interval of time $10s$ . Coefficient of kinetic friction is (given, $g = 10ms^{-2}$ )
A.
0.60
B.
0.75
C.
0.50
D.
0.25
JEE (Main) June 2022 Q44 Errorless 7. Critical Thinking 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) June 2022 Q45 Errorless 7. Critical Thinking MCQ
A block of mass M placed inside a box descends vertically with acceleration ā€˜aā€™. The block exerts a force equal to one-fourth of its weight on the floor of the box. The value of ā€˜aā€™ will be
A.
$\frac{g}{4}$
B.
$\frac{g}{2}$
C.
$\frac{3g}{4}$
D.
g
JEE (Main) June 2022 Q46 Errorless 7. Critical Thinking MCQ
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 Q47 Errorless 7. Critical Thinking MCQ
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 Q48 Errorless 7. Critical Thinking MCQ
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 Q49 Errorless 7. Critical Thinking MCQ
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 Q50 Errorless 7. Critical Thinking MCQ
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