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2046 Q1 Advance 1. SINGLE CORRECT CHOICE TYPE QUESTIONS MCQ
A chain consisting of 5 links each of mass $0.1\mathrm{kg}$ is lifted vertically with a constant acceleration of $2.5\mathrm{ms}^{-2}$ . The force of interaction between the top link and the link immediately below it, will be
A.
$6.15\mathrm{N}$
B.
$4.92\mathrm{N}$
C.
$3.69\mathrm{N}$
D.
$2046\mathrm{N}$
Online April 2019 Q2 Advance 7. ARCHIVE: JEE MAIN MCQ
If $10^{22}$ gas molecules each of mass $10^{-26}$ kg collide with a surface (perpendicular to it) elastically per second over an area $1\mathrm{m}^2$ with a speed $10^{4}\mathrm{ms}^{-1}$ , the pressure exerted by the gas molecules will be of the order of
A.
$1\mathrm{Nm}^{-2}$
B.
$2\mathrm{Nm}^{-2}$
C.
$3\mathrm{Nm}^{-2}$
D.
$4\mathrm{Nm}^{-2}$
Online April 2019 Q3 Advance 7. ARCHIVE: JEE MAIN MCQ
A ball is thrown vertically up (taken as +z-axis) from the ground. The correct momentum height $(p-h)$ diagram is
A.
B.
C.
D.
Online April 2019 Q4 Advance 7. ARCHIVE: JEE MAIN 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, v 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.
$\frac{1}{\sqrt{\gamma g}}\ln \left(1 + \sqrt{\frac{\gamma}{g}} V_0\right)$
C.
$\frac{1}{\sqrt{\gamma g}}\tan^{-1}\left(\sqrt{\frac{\gamma}{g}}V_{0}\right)$
D.
$\frac{1}{\sqrt{2\gamma g}}\tan^{-1}\left(\sqrt{\frac{2\gamma}{g}} V_0\right)$
Online April 2019 Q5 Advance 7. 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 Q6 Advance 7. 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 Q7 Advance 7. 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 Q8 Advance 7. 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 Q9 Advance 7. 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 Q10 Advance 7. 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 Q11 Advance 7. 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 Q12 Advance 7. 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 Q13 Advance 7. 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.
$\frac{2}{3}$
2018 Q14 Advance 7. 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 Q15 Advance 7. 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 Q16 Advance 7. 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 Q17 Advance 8. 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 Q18 Advance 7. 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 Q19 Advance 7. 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.
$4\mathrm{ms}^{-1}$
Online 2016 Q20 Advance 7. ARCHIVE: JEE MAIN 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 $\mu_{min}$ between the mass and the inclined surface such that the mass does not move is
A.
$\tan2\theta$
B.
$\tan\theta$
C.
$3\tan\theta$
D.
$2\tan\theta$
Online 2016 Q21 Advance 7. ARCHIVE: JEE MAIN MCQ
A particle of mass m is acted upon by a force F given by the empirical law $F = \frac{R}{t^{2}} v(t)$ . If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot (A) $\log v(t)$ against $\frac{1}{t}$
A.
$\log v(t)$ against $\frac{1}{t}$
B.
$v(t)$ against $t^{2}$
C.
$\log v(t)$ against $\frac{1}{t^{2}}$
D.
$\log v(t)$ against t
JEE (Advanced) 2016 Q22 Advance 8. ARCHIVE: JEE ADVANCED MCQ
A uniform wooden stick of mass 1.6 kg and length l rests in an inclined manner on a smooth, vertical wall of height $h(
A.
$\frac {h}{l} = \frac {\sqrt {3}}{1 6}, f = \frac {1 6 \sqrt {3}}{3} \mathrm{N}$
B.
$\frac {h}{l} = \frac {3}{1 6}, f = \frac {1 6 \sqrt {3}}{3} \mathrm{N}$
C.
$\frac{h}{l}=\frac{3\sqrt{3}}{16},\quad f=\frac{8\sqrt{3}}{3},\text{N}$
D.
$\frac{h}{l}=\frac{3\sqrt{3}}{16},\quad f=\frac{16\sqrt{3}}{3},\text{N}$
2015 Q23 Advance 7. ARCHIVE: JEE MAIN MCQ
Given in the figure are two blocks $A$ and $B$ of weight $20\mathrm{N}$ and $100\mathrm{N}$ , 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.
$120\mathrm{N}$
B.
$150\mathrm{N}$
C.
$100\mathrm{N}$
D.
$80\mathrm{N}$
Online 2015 Q24 Advance 7. ARCHIVE: JEE MAIN MCQ
A block of mass m = 10 kg rests on a horizontal table. The coefficient of friction between the block and the table is 0.05. When hit by a bullet of mass 50 g moving with speed v, that gets embedded in it, the block moves and comes to stop after moving a distance of 2 m on the table. If a freely falling object were to acquire speed $\frac{v}{10}$ after being dropped from height H, then neglecting energy losses and taking $g = 10 \, ms^{-2}$ , the value of H is close to
A.
0.2 km
B.
0.3 km
C.
0.04 km
D.
0.5 km
Online 2015 Q25 Advance 7. ARCHIVE: JEE MAIN MCQ
A large number (n) of identical beads, each of mass m and radius r are strung on a thin smooth rigid horizontal rod of length $L(L \gg r)$ and are at rest at random positions. The rod is mounted between two rigid supports (shown in figure). If one of the beads is now given a speed v, the average force experienced by each support after a long time is (assume all collisions are elastic)
A.
$\frac{mv^2}{L - nr}$
B.
$\frac{mv^2}{L - 2nr}$
C.
$\frac{mv^2}{2(L - nr)}$
D.
zero