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255 Questions Start Errorless Test
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JEE (Main) Jan. 2025 Q1 Errorless 7. Critical Thinking MCQ
A balloon and its content having mass M is moving up with an acceleration ā€˜aā€™. The mass that must be released from the content so that the balloon starts moving up with an acceleration ā€˜3aā€™ will be : (Take ā€˜gā€™ as acceleration due to gravity)
A.
$\frac{3Ma}{2a-g}$
B.
$\frac{3Ma}{2a+g}$
C.
$\frac{2Ma}{3a+g}$
D.
$\frac{2Ma}{3a-g}$
JEE (Main) Jan. 2025 Q2 Errorless 7. Critical Thinking MCQ
A sand dropper drops sand of mass $m(t)$ on a conveyor belt at a rate proportional to the square root of speed $(v)$ of the belt, i.e. $\frac{dm}{dt} \propto \sqrt{v}$ . If $P$ is the power delivered to run the belt at constant speed then which of the following relationship is true
A.
$P^2 \propto v^3$
B.
$P \propto \sqrt{v}$
C.
$P \propto v$
D.
$P^2 \propto v^5$
JEE (Main) Jan. 2024 Q3 Errorless 7. Critical Thinking MCQ
A spherical body of mass 100g is dropped from a height of 10m from the ground. After hitting the ground, the body rebounds to a height of 5m. The impulse of force imparted by the ground to the body is given by (given $g = 9.8 \, m/s^{2}$ )
A.
$4.32 \, kg \, ms^{-1}$
B.
$43.2 \, kg \, ms^{-1}$
C.
$23.9 \, kg \, ms^{-1}$
D.
$2.39 \, kg \, ms^{-1}$
JEE (Main) Jan. 2024 Q4 Errorless 7. Critical Thinking MCQ
Three blocks A, B and C are pulled on a horizontal smooth surface by a force of 80 N as shown in figure image.png The tensions $T_{1}$ and $T_{2}$ in the string are respectively
A.
40N, 64N
B.
60N, 80N
C.
88N, 96N
D.
80N, 100N
JEE (Main) Jan. 2024 Q5 Errorless 7. Critical Thinking MCQ
A light string passing over a smooth light fixed pulley connects two blocks of masses $m_{1}$ and $m_{2}$ . If the acceleration of the system is g/8, then the ratio of masses is
A.
$\frac{9}{7}$
B.
$\frac{8}{1}$
C.
$\frac{4}{3}$
D.
$\frac{5}{3}$
JEE (Main) Jan. 2024 Q6 Errorless 7. Critical Thinking MCQ
A cricket player catches a ball of mass 120 g moving with 25 m/s speed. If the catching process is completed in 0.1 s then the magnitude of force exerted by the ball on the hand of player will be (in SI unit)
A.
24
B.
12
C.
25
D.
30
JEE (Main) Jan. 2024 Q7 Errorless 7. Critical Thinking MCQ
A body of mass 4 kg experiences two forces $\vec{F}_1 = 5\hat{i} + 8\hat{j} + 7\hat{k}$ and $\vec{F}_2 = 3\hat{i} - 4\hat{j} - 3\hat{k}$ . The acceleration acting on the body is
A.
$-2\hat{i} - \hat{j} - \hat{k}$
B.
$4\hat{i} + 2\hat{j} + 2\hat{k}$
C.
$2\hat{i} + \hat{j} + \hat{k}$
D.
$2\hat{i} + 3\hat{j} + 3\hat{k}$
JEE (Main) Jan. 2024 Q8 Errorless 7. Critical Thinking MCQ
All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass 2 kg is
A.
g
B.
$\frac{g}{3}$
C.
$\frac{g}{2}$
D.
$\frac{g}{4}$
JEE (Main) April 2024 Q9 Errorless 7. Critical Thinking MCQ
A wooden block of mass 5 kg rests on soft horizontal floor. When an iron cylinder of mass 25 kg is placed on the top of the block, the floor yields and the block and the cylinder together go down with an acceleration of $0.1 \, ms^{-2}$ . The action force of the system on the floor is equal to
A.
297 N
B.
294 N
C.
291 N
D.
196 N
JEE (Main) April 2024 Q10 Errorless 7. Critical Thinking MCQ
A body of weight 200 N is suspended from a tree branch thought a chain of mass 10 kg. The branch pulls the chain by a force equal to (if $g = 10 \, m/s^{2}$ )
A.
150 N
B.
300 N
C.
200 N
D.
100 N
JEE (Main) April 2024 Q11 Errorless 7. Critical Thinking MCQ
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
A.
$\frac{\sqrt{2}-1}{\sqrt{2}+1}$
B.
$\frac{1+\sqrt{5}}{\sqrt{5}-1}$
C.
$\frac{1+\sqrt{5}}{\sqrt{2}-1}$
D.
$\frac{\sqrt{3}+1}{\sqrt{2}-1}$
JEE (Main) April 2024 Q12 Errorless 7. Critical Thinking MCQ
A player caught a cricket ball of mass 150 g moving at a speed of 20 m/s. If the catching process is completed in 0.1 s, the magnitude of force exerted by the ball on the hand of the player is
A.
150 N
B.
3 N
C.
30 N
D.
300 N
JEE (Main) April 2024 Q13 Errorless 8. Graphical Questions MCQ
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
A.
B.
C.
D.
JEE (Main) Jan. 2024 Q14 Errorless 14. Critical Thinking-friction MCQ
Consider a block and trolley system as shown in figure. If the coefficient of kinetic friction between the trolley and the surface is 0.04, the acceleration of the system in $ms^{-2}$ is (Consider that the string is massless and unstretchable and the pulley is also massless and frictionless)
A.
3
B.
4
C.
2
D.
1.2
JEE (Main) Jan. 2024 Q15 Errorless 14. Critical Thinking-friction MCQ
Given below are two statements: Statement I: The limiting force of static friction depends on the area of contact and independent of materials. Statement II: The limiting force of kinetic friction is independent of the area of contact and depends on materials. In the light of the above statements, choose the most appropriate answer from the options given below
A.
If both assertion and reason are true and the reason is the correct explanation of the assertion.
B.
If both assertion and reason are true but reason is not the correct explanation of the assertion.
C.
If assertion is true but reason is false.
D.
If the assertion and reason both are false.
E.
If assertion is false but reason is true.
JEE (Main) Jan. 2024 Q16 Errorless 14. Critical Thinking-friction MCQ
A block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of $60^{\circ}$ by a force of 10 N parallel to the inclined surface as shown in figure. When the block is pushed up by 10 m along inclined surface, the work done against frictional force is $[g = 10m/s^{2}]$
A.
$5\sqrt{3} J$
B.
$5J$
C.
$5\times 10^{3}J$
D.
$10J$
JEE (Main) Jan. 2024 Q17 Errorless 14. Critical Thinking-friction MCQ
A block of mass m is placed on a surface having vertical cross section given by $y = x^{2}/4$ . If coefficient of friction is 0.5, the maximum height above the ground at which block can be placed without slipping is
A.
1/4m
B.
1/2m
C.
1/6m
D.
1/3m
JEE (Main) Jan. 2024 Q18 Errorless 14. Critical Thinking-friction MCQ
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 kg will move down with an acceleration of $2m/s^{2}$ , is (take $g=10m/s^{2}$ and $\tan37^{\circ}=3/4$ )
A.
9 kg
B.
4.5 kg
C.
6.5 kg
D.
2.25 kg
JEE (Main) Jan. 2024 Q19 Errorless 14. Critical Thinking-friction MCQ
A coin is placed on a disc. The coefficient of friction between the coin and the disc is $\mu$ . If the distance of the coin from the center of the disc is $r$ , the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is
A.
$\frac{\mu g}{r}$
B.
$\sqrt{\frac{r}{\mu g}}$
C.
$\sqrt{\frac{\mu g}{r}}$
D.
$\frac{\mu}{\sqrt{rg}}$
JEE (Main) Jan. 2024 Q20 Errorless 14. Critical Thinking-friction MCQ
A block of mass 100 kg slides over a distance of 10 m on a horizontal surface. If the co-efficient of friction between the surfaces is 0.4, then the work done against friction (in J) is
A.
4200
B.
3900
C.
4000
D.
4500
JEE (Main) April 2024 Q21 Errorless 14. Critical Thinking-friction MCQ
A 2 kg brick begins to slide over a surface which is inclined at an angle of $45^{\circ}$ with respect to horizontal axis. The co-efficient of static friction between their surface is
A.
1
B.
$\frac{1}{\sqrt{3}}$
C.
0.5
D.
1.7
JEE (Main) April 2024 Q22 Errorless 14. Critical Thinking-friction MCQ
A heavy box of mass 50 kg is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is 0.3 then force of kinetic friction is
A.
14.7 N
B.
147 N
C.
1.47 N
D.
1470 N
JEE (Main) Jan. 2023 Q23 Errorless 7. Critical Thinking MCQ
Given below are two statements: Statement-I: An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable. Statement-II : Force exerted by the floor of an elevator on the foot of a person standing on it is more than his/her weight when the elevator goes down with increasing speed. In the light of the above statements, choose the correct answer from the options given below
A.
If both assertion and reason are true and the reason is the correct explanation of the assertion.
B.
If both assertion and reason are true but reason is not the correct explanation of the assertion.
C.
If assertion is true but reason is false.
D.
If the assertion and reason both are false.
E.
If assertion is false but reason is true.
JEE (Main) Jan. 2023 Q24 Errorless 7. Critical Thinking 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 $g = 10m/s^{2}$ )
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) Jan. 2023 Q25 Errorless 7. Critical Thinking MCQ
A car is moving with a constant speed of $20m/s$ in a circular horizontal track of radius $40m$ . A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be $(Take g = 10m/s^2)$
A.
$\frac{\pi}{6}$
B.
$\frac{\pi}{2}$
C.
$\frac{\pi}{4}$
D.
$\frac{\pi}{3}$