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968 Questions Start Allen Test
All Exams Allen Advance Errorless
Online April 2019 Q126 Advance ARCHIVE: JEE MAIN 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 $g=10\ ms^{-2}$ ]
A.
40 N
B.
12N
C.
16 N
D.
8 N
Online April 2019 Q127 Advance ARCHIVE: JEE MAIN MCQ
[Online April 2019] A block of mass 5 is kg (i) pushed in case (A) and (ii) pulled in case (B), by a force $F = 20 \, \text{N}$ , making an angle of $30^\circ$ with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is $\mu = 0.2$ . The difference between the accelerations of the block, in case (B) and case (A) will be $(g = 10 \, \text{ms}^{-2})$
A.
C.
$0 \, ms^{-2}$
D.
$0.8 \, ms^{-2}$
Online April 2019 Q128 Advance ARCHIVE: JEE MAIN 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 $\frac{k_1}{k_2}$ of the corresponding force constants, $k_{1}$ and $k_{2}$ will be
A.
$n^2$
B.
$\frac{1}{n^2}$
C.
$n$
D.
$\frac{1}{n}$
Online April 2019 Q129 Advance ARCHIVE: JEE MAIN MCQ
A smooth wire of length $2\pi r$ is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed $\omega$ about the vertical diameter AB, as shown in figure, the bead is at rest with respect to the circular ring at position P as shown. Then the value of $\omega^{2}$ is equal to
A.
$\frac{(g\sqrt{3})}{r}$
B.
$\frac{2g}{r}$
C.
$\frac{2g}{(r\sqrt{3})}$
D.
$\frac{\sqrt{3}g}{2r}$
Online January 2019 Q130 Advance ARCHIVE: JEE MAIN MCQ
A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force P, such that the block does not move downward? (Take $g = 10 \, ms^{-2}$ )
A.
25 N
B.
32 N
C.
18 N
D.
23 N
Online January 2019 Q131 Advance ARCHIVE: JEE MAIN MCQ
A mass of $10\mathrm{kg}$ is suspended vertically by a rope from the roof. When a horizontal force is applied on the roof at some point, the rope deviated at an angle of $45^{\circ}$ at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is $(g = 10\mathrm{ms}^{-2})$
A.
$100\mathrm{N}$
B.
$200\mathrm{N}$
C.
$70\mathrm{N}$
D.
$140\mathrm{N}$
Online January 2019 Q132 Advance ARCHIVE: JEE MAIN MCQ
A particle of mass m is moving in a straight line with momentum p. Starting at time t = 0, a force F = kt acts in the same direction on the moving particle during time interval T so that its momentum changes from p to 3p. Here k is a constant. The value of T is
A.
$\sqrt{\frac{2k}{p}}$
B.
$2\sqrt{\frac{p}{k}}$
C.
$\sqrt{\frac{2p}{k}}$
D.
$2\sqrt{\frac{k}{p}}$
Online January 2019 Q133 Advance ARCHIVE: JEE MAIN MCQ
A particle moves from the point $(2.0\hat{i}+4.0\hat{j})$ m, at t=0, with an initial velocity $(5.0\hat{i}+4.0\hat{j})$ ms $^{-1}$ . It is acted upon by a constant force which produces a constant acceleration $(4.0\hat{i}+4.0\hat{j})$ ms $^{-2}$ . What is the distance of the particle from the origin at time 2 s?
A.
$20\sqrt{2}$ m
B.
15 m
C.
$10\sqrt{2}$ m
D.
5 m
Online January 2019 Q134 Advance ARCHIVE: JEE MAIN MCQ
A block kept on a rough inclined plane, as shown in the figure, remains at rest up to a maximum force $2\mathrm{N}$ down the inclined plane. The maximum external force up the inclined plane that does not move the block is $10\mathrm{N}$ . The coefficient of static friction between the block and the plane is [Take $g = 10~\mathrm{ms}^{-2}$ ]
A.
$\frac{1}{2}$
B.
$\frac{\sqrt{3}}{2}$
C.
$\frac{\sqrt{3}}{4}$
D.
$\frac{2}{3}$
JEE (Main) 2018 Q135 Allen 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) 2018 Q136 Errorless Conservation of Linear Momentum and Impulse MCQ
The mass of a hydrogen molecule is $3.32 \times 10^{-27}$ kg. If $10^{23}$ hydrogen molecules strike, per second, a fixed wall of area $2 cm^{2}$ at an angle of $45^{\circ}$ to the normal, and rebound elastically with a speed of $10^{3}$ m/s, then the pressure on the wall is nearly
A.
$4.70 \times 10^{3}$ N/m $^{2}$
B.
$2.35 \times 10^{2}$ N/m $^{2}$
C.
$4.70 \times 10^{2}$ N/m $^{2}$
D.
$2.35 \times 10^{3}$ N/m $^{2}$
JEE (Advanced) 2018 Q137 Errorless JEE Section Numerical
A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass $m = 0.4\mathrm{kg}$ is at rest on this surface. An impulse of $1.0N s$ is applied to the block at time to $t = 0$ so that it starts moving along the x-axis with a velocity $v(t) = v_0e^{-t / \tau}$ , where $v_0$ is a constant and $\tau = 4s$ . The displacement of the block, in metres, at $t = \tau$ is ____ Take $e^{-1} = 0.37$
NEET 2018 Q138 Errorless Kinetic Friction MCQ
Which one of the following statements is incorrect
A.
Rolling friction is smaller than sliding friction
B.
Limiting value of static friction is directly proportional to normal reactions
C.
Frictional force opposes the relative motion
D.
Coefficient of sliding friction has dimensions of length
2018 Q139 Advance ARCHIVE: JEE MAIN 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.
$18.3\mathrm{kg}$
B.
$27.3\mathrm{kg}$
C.
$43.3\mathrm{kg}$
D.
$10.3\mathrm{kg}$
Online 2018 Q140 Advance ARCHIVE: JEE MAIN MCQ
A given object takes n times more time to slide down a $45^{\circ}$ rough inclined plane as it takes to slide down a perfectly smooth $45^{\circ}$ incline. The coefficient of kinetic friction between the object and the incline is
A.
$\sqrt{1-\frac{1}{n^{2}}}$
B.
$1-\frac{1}{n^{2}}$
C.
$\frac{1}{2-n^{2}}$
D.
$\sqrt{\frac{1}{1-n^{2}}}$
Online 2018 Q141 Advance ARCHIVE: JEE MAIN MCQ
A body of mass 2 kg slides down with an acceleration of $3 \, ms^{-2}$ on a rough inclined plane having a slope of $30^{\circ}$ . The external force required to take the same body up the plane with the same acceleration will be $(g = 10 \, \text{ms}^{-2})$
A.
6 N
B.
14 N
C.
4 N
D.
20 N
JEE (Advanced) 2018 Q142 Advance ARCHIVE: JEE ADVANCED Numerical
A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass $m = 0.4 \, \mathrm{kg}$ is at rest on this surface. An impulse of 1 Ns is applied to the block at time $t = 0$ , so that it starts moving along the X-axis with a velocity $v(t) = v_0 e^{-t / \tau}$ , where $v_0$ is a constant and $\tau = 4 \, \mathrm{s}$ . The displacement of the block, in metres, at $t = \tau$ is ...... (Take, $e^{-1} = 0.37$ ) [Round off your answer to nearest integer].
Online 2017 Q143 Advance ARCHIVE: JEE MAIN MCQ
Two particles $A$ and $B$ of equal mass $M$ are moving with the same speed $v$ as shown in the figure. They collide completely inelastically and move as a single particle $C$ . The angle $\theta$ that the path, $C$ makes with the X-axis is given by
A.
$\tan\theta=\frac{\sqrt{3}+\sqrt{2}}{1-\sqrt{2}}$
B.
$\tan\theta=\frac{1-\sqrt{3}}{1+\sqrt{2}}$
C.
$\tan\theta=\frac{\sqrt{3}-\sqrt{2}}{1-\sqrt{2}}$
D.
$\tan\theta=\frac{1-\sqrt{2}}{\sqrt{2}(1+\sqrt{3})}$
Online 2017 Q144 Advance ARCHIVE: JEE MAIN MCQ
A conical pendulum of length 1 m makes an angle $\theta = 45^{\circ}$ w.r.t. Z-axis and moves in a circle in the XY plane. The radius of the circle is 0.4 m and its center is vertically below O. The speed of the pendulum, in its circular path, will be (Take $g = 10 \, ms^{-2}$ )
A.
$0.4\mathrm{ms}^{-1}$
B.
$2\mathrm{ms}^{-1}$
C.
$0.2\mathrm{ms}^{-1}$
D.
$4\mathrm{ms}^{-1}$
JEE (Main) 2016 Q145 Allen 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.
$\tan 2\theta$
WB-JEE 2016 Q146 Errorless Conservation of Linear Momentum and Impulse MCQ
An explosive of mass 9 kg is divided in two parts. One part of mass 3 kg moves with velocity of 16 m/s. The kinetic energy of other part will be
A.
192 J
B.
162 J
C.
150 J
D.
200 J
NEET (Phase-II) 2016 Q147 Errorless Conservation of Linear Momentum and Impulse MCQ
A rigid ball of mass m strikes a rigid wall at $60^{\circ}$ and gets reflected without loss of speed as shown in the figure below. The value of impulse imparted by the wall in the ball will be
A.
$\frac{mV}{3}$
B.
mV
C.
2mV
D.
$\frac{mV}{2}$
WB-JEE 2016 Q148 Errorless Static and Limiting Friction MCQ
A mass m rests on another mass M. The co-efficient of static friction between B the surfaces of m and M is $\mu$ . M rests on a smooth frictionless horizontal plane. The maximum force applied horizontally on M for which m will move along with M without slipping is
A.
$mg + \mu mg$
B.
$(M + m)\mu g$
C.
$\frac{mM}{M + m}\mu g$
D.
$\mu mg$
NEET (Phase-I) 2016; JEE (Main) April 2024, Jan. 2025 Q149 Errorless Motion on Inclined Surface MCQ
A car is negotiating a curved road of radius R. The road is banked at an angle $\theta$ . The coefficient of friction between the tyres of the car and the road is $\mu_{s}$ . The maximum safe velocity on this road is
A.
$\sqrt{gR^{2}\frac{\mu_{s}+\tan\theta}{1-\mu_{s}\tan\theta}}$
B.
$\sqrt{gR\frac{\mu_{s}+\tan\theta}{1-\mu_{s}\tan\theta}}$
C.
$\sqrt{\frac{g}{R}\frac{\mu_{s}+\tan\theta}{1-\mu_{s}\tan\theta}}$
D.
$\sqrt{\frac{g}{R^{2}}\frac{\mu_{s}+\tan\theta}{1-\mu_{s}\tan\theta}}$
JEE (Advanced) 2016 Q150 Errorless Critical Thinking-friction MCQ
A uniform wooden stick of mass 1.6kg and length $\ell$ rests in an inclined manner on a smooth, vertical wall of height $h(<\ell)$ such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of $30^{\circ}$ with the wall and bottom of the stick is on a rough floor. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the stick. The ratio $h/\ell$ and the frictional force $f$ at the bottom of the stick are $(g=10ms^{-2})$ (Take the normal reaction at the wall equal to the normal reaction at the floor)
A.
$\frac{h}{\ell}=\frac{\sqrt{3}}{16}, f=\frac{16\sqrt{3}}{3}N$
B.
$\frac{h}{\ell}=\frac{3}{16}, f=\frac{16\sqrt{3}}{3}N$
C.
$\frac{h}{\ell}=\frac{3\sqrt{3}}{16}, f=\frac{8\sqrt{3}}{3}N$
D.
$\frac{h}{\ell}=\frac{3\sqrt{3}}{16}, f=\frac{16\sqrt{3}}{3}N$