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All Exams Allen Advance Errorless
Online 2016 Q151 Advance 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 Q152 Advance 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 Q153 Advance 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.
$\frac{h}{l}=\frac{3\sqrt{3}}{16},\quad f=\frac{16\sqrt{3}}{3},\text{N}$
JEE (Main) 2015 Q154 Allen JEE Main PYQ MCQ
Given in the figure are two blocks A and B of weight 20N and 100N, 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 N
B.
150 N
C.
100 N
D.
80 N
WB-JEE 2015 Q155 Errorless Static and Limiting Friction MCQ
Block B lying on a table weighs W. The coefficient of static friction between the block and the table is $\mu$ . Assume that the cord between and the knot is horizontal. The maximum weight of the block A for which the system will be stationary is
A.
$\frac{W\tan\theta}{\mu}$
B.
$\mu W\tan\theta$
C.
$\mu W\sqrt{1+\tan^{2}\theta}$
D.
$\mu W\sin\theta$
JEE (Main) 2015 Q156 Errorless Static and Limiting Friction MCQ
Given in the figure are two blocks A and B of weight 20 N and 100 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.
100 N
B.
80 N
C.
120 N
D.
150 N
GUJCET 2015 Q157 Errorless Motion on Inclined Surface MCQ
An inclined plane of length 5.60 m making an angle of $45^{\circ}$ with the horizontal is placed in an uniform electric field $E = 100 Vm^{-1}$ . A particle of mass 1 kg and charge $10^{-2} C$ is allowed to slide down from rest position from maximum height of slope. If the co-efficient of friction is 0.1, the time taken by the particle to reach the bottom is
A.
1 s
B.
1.41 s
C.
2 s
D.
None of these
2015 Q158 Advance 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 Q159 Advance 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 Q160 Advance 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
JEE (Main) 2014 Q161 Allen JEE Main PYQ MCQ
A block of mass m is placed on a surface with a vertical cross section given by $y=\frac{x^{3}}{6}$ . If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is :-
A.
$\frac{1}{3}m$
B.
$\frac{1}{2}m$
C.
$\frac{1}{6}m$
D.
$\frac{2}{3}m$
JEE (Advanced) 2014 Q162 Allen JEE Advanced PYQ Match the Columns
A block of mass $m_{1} = 1kg$ another mass $m_{2} = 2kg$ , are placed together (see figure) on an inclined plane with angle of inclination $\theta$ . Various values of $\theta$ are given in Column-I. The coefficient of friction between the block $m_{1}$ and the plane is always zero. The coefficient of static and dynamic friction between the block $m_{2}$ and the plane are equal to $\mu = 0.3$ . In Column-II expressions for the friction on block $m_{2}$ are given. Match the correct expression of the friction in Column-II with the angles given in Column-I and choose the correct option. The acceleration due to gravity is denoted by g.

[Useful information : tan (5.5°) ≈ 0.1 ; tan(11.5°) ≈ 0.2 ; tan (16.5°) ≈ 0.3]

Column-IColumn-II
(P)$m_{2}g \sin \theta$
(Q)$(m_{1} + m_{2})g\sin \theta$
(R)$\mu m_{2}g\cos \theta$
(S)$\mu (m_1 + m_2)g\cos \theta$
(I)$\theta = 5^{\circ}$
(II)$\theta = 10^{\circ}$
(III)$\theta = 15^{\circ}$
(IV)$\theta = 20^{\circ}$
A.
I-P, II-P, III-P, IV-R
B.
I-Q, II-Q, III-Q, IV-R
C.
I-Q, II-Q, III-Q, IV-S
D.
I-Q, II-Q, III-R, IV-R
CBSE PMT 2014 Q163 Errorless Second Law of Motion MCQ
A balloon with mass m is descending down with an acceleration a (where a < g). How much mass should be removed from it so that it starts moving up with an acceleration a
A.
$\frac{ma}{g+a}$
B.
$\frac{ma}{g-a}$
C.
$\frac{2ma}{g+a}$
D.
$\frac{2ma}{g-a}$
CBSE PMT 2014 Q164 Errorless Graphical Questions MCQ
A body of mass 3kg is acted on by a force which varies as shown in the graph below. The momentum acquired is given by
A.
Zero
B.
5 N-s
C.
30 N-s
D.
50 N-s
JEE (Advanced) 2014 Q165 Errorless Matrix Match Type Questions Numerical
A person in a lift is holding a water jar, which has a small hole at the lower end of its side. When the lift is at rest, the water jet coming out of the hole hits the floor of the lift at a distance d of 1.2 m from the person. In the following, state of the lift's motion is given in Column-I and the distance where the water jet hits the floor of the lift is given in Column-II. Match the statements from Column-I with those in Column-II and select the correct answer using the code given below the columns
Column-IColumn-II
(A)Lift is accelerating vertically up
(B)Lift is accelerating vertically down with an accelerating less than the gravitational acceleration
(C)Lift is moving vertically up with constant Speed
(D)Lift is falling freely
(P)d = 1.2 m
(Q)d > 1.2 m
(R)d < 1.2 m
(S)No water leaks out of the jar
CBSE PMT 2014 Q166 Errorless Static and Limiting Friction MCQ
A system consists of three masses $m_{1}$ , $m_{2}$ and $m_{3}$ connected by a string passing over a pulley P. The mass $m_{1}$ hangs freely and $m_{2}$ and $m_{3}$ are on a rough horizontal table (the coefficient of friction = $\mu$ ). The pulley is frictionless and of negligible mass. The downward acceleration of mass $m_{1}$ is (Assume $m_{1} = m_{2} = m_{3} = m$ )
A.
$g(1-2\mu)/3$
B.
$g(1 - 2\mu) / 2$
C.
$g(1-g\mu)/9$
D.
$2g\mu /3$
JEE (Advanced) 2014 Q167 Errorless Matrix Match Type Questions-friction Numerical
A block of mass $m_{1}=1kg$ another mass $m_{2}=2kg$ , are placed together (see figure) on an inclined plane with angle of inclination $\theta$ . Various values of $\theta$ are given in Column-I. The coefficient of friction between the block $m_{1}$ and the Plane is always zero. The coefficient of static and dynamic friction between the block $m_{2}$ and the plane are equal to $\mu=0.3$ . In Column-II expression for the friction on block $m_{2}$ given. Match the correct expression of the friction in Column-II with the angles given in Column-I, and choose the correct option. The acceleration due to gravity is denoted by g
[Useful information : $\tan(5.5^{\circ})\approx0.1;\tan(11.5^{\circ})\approx0.2;$
$\tan (16.5^{\circ}\approx 0.3)]$
Column-IColumn-II
(A)$\theta = 5^{\circ}$
(B)$\theta = 10^{\circ}$
(C)$\theta = 15^{\circ}$
(D)$\theta = 20^{\circ}$
(P)$m_{2}g\sin \theta$
(Q)$(m_{1} + m_{2})g\sin \theta$
(R)$\mu m_{2}g\cos \theta$
(S)$\mu (m_1 + m_2)g\cos \theta$
2014 Q168 Advance ARCHIVE: JEE MAIN MCQ
A block of mass m is placed on a surface with a vertical cross section given by $y = \frac{x^{3}}{6}$ . If the coefficient of friction is 0.5, the maximum height above the ground at which the block can be placed without slipping is
A.
$\frac{1}{2}m$
B.
$\frac{1}{6}m$
C.
$\frac{2}{3}m$
D.
$\frac{1}{3}m$
JEE (Advanced) 2014 Q169 Advance ARCHIVE: JEE ADVANCED Match the Columns
A block of mass $m_{1}=1$ kg another mass $m_{2}=2$ kg are placed together (shown in figure) on an inclined plane with angle of inclination $\theta$ . Various values of $\theta$ are given in Column-I. The coefficient of friction between the block $m_{1}$ and the plane is always zero. The coefficient of static and dynamic friction between the block $m_{2}$ and the plane are equal to $\mu=0.3$ .




In Column-II expressions for the friction on the block $m_{2}$ are given. Match the correct expression of the friction in Column-II with the angles given in Column-I and choose the correct option. The acceleration due to gravity is denoted by g.

(Useful information $\tan(5.5^{\circ})\approx0.1$ ; $\tan(11.5^{\circ})\approx0.2$ ; $\tan(16.5^{\circ})\approx0.3$ )
Column-IColumn-II
(P)$\theta = 5^\circ$
(Q)$\theta = 10^\circ$
(R)$\theta = 15^\circ$
(S)$\theta = 20^\circ$
(I)$m_2g\sin\theta$
(II)$(m_1+m_2)g\sin\theta$
(III)$\mu m_2g\cos\theta$
(IV)$\mu(m_1+m_2)g\cos\theta$
A.
P-1, Q-1, R-1, S-3
B.
P-2, Q-2, R-2, S-3
C.
P-2, Q-2, R-2, S-4
D.
P-2, Q-2, R-3, S-3
JEE (Advanced) 2014 Q170 Advance ARCHIVE: JEE ADVANCED MSQ
In the figure, a ladder of mass m is shown leaning against a wall. It is in static equilibrium making an angle $\theta$ with the horizontal floor. The coefficient of friction between the wall and the ladder is $\mu_{1}$ and that between the floor and the ladder is $\mu_{2}$ . The normal reaction of the wall on the ladder is $N_{1}$ and that of the floor is $N_{2}$ . If the ladder is about to slip, then
A.
$\mu_{1} = 0, \mu_{2} \neq 0$ and $N_{2}\tan \theta = \frac{mg}{2}$
B.
$\mu_{1} \neq 0$ , $\mu_{2} = 0$ and $N_{1} \tan \theta = \frac{mg}{2}$
C.
$\mu_{1} \neq 0, \mu_{2} \neq 0$ and $N_{2} = \frac{mg}{1 + \mu_{1}\mu_{2}}$
D.
$\mu_{1} = 0, \mu_{2} \neq 0$ and $N_{1}\tan \theta = \frac{mg}{2}$
WB-JEE 2013 Q171 Errorless Conservation of Linear Momentum and Impulse MCQ
A shell of mass 5M, acted upon by no external force and initially at rest, bursts into three fragments of masses M, 2M and 2M respectively. The first two fragments move in opposite directions with velocities of magnitudes 2V and V respectively. The third fragment will
A.
Move with a velocity V in a direction perpendicular to the other two
B.
Move with a velocity 2V in the direction of velocity of the first fragment
C.
Be at rest
D.
Move with a velocity V in the direction of velocity of the second fragment
NEET 2013 Q172 Errorless Motion of Connected Bodies MCQ
Three blocks with masses m, 2m and 3m are connected by strings, as shown in figure. After an upward force F is applied on block m, the masses move upward at constant speed v. What is the net force on the block of mass 2m (g is the acceleration du+e to gravity)
A.
6 mg
B.
Zero
C.
2 mg
D.
3 mg
WB-JEE 2013 Q173 Errorless JEE Section MSQ
A block of mass $m(=0.1kg)$ is hanging over a frictionless light fixed pulley by an inextensible string of negligible mass. The other end of the string is pulled by a constant force F in the vertically downward direction. The linear momentum of the block increase by $2kg\,ms^{-1}$ in 1 s after the block starts from rest. Then, (given $g=10\,ms^{-2}$ )
A.
The tension in the string is $F$
B.
The tension in the string is $3N$
C.
The work done by the tension on the block is $20J$ during this 1 s
D.
The work done against the force of gravity is 10 J
MP PET 2013 Q174 Errorless Motion on Inclined Surface MCQ
A cylinder rolls up an inclined plane, reaches some height and then rolls down without slipping throughout these motions. The directions of the frictional force acting on the cylinder are
A.
Up the incline while ascending and down the incline while descending
B.
Up the incline while descending and down the incline while ascending
C.
Down the incline while ascending and descending
D.
Up the incline while ascending and descending
AMU (Engg.) 2012 Q175 Errorless Second Law of Motion MCQ
A body of mass 0.4 kg starting at origin at t=0 with a speed of 10 m/s in the positive x-axis direction is subjected to a constant force F=8 N towards negative x-axis. Calculate the position of the particle after 25 seconds
A.
-6000 m
B.
-8000 m
C.
+4000 m
D.
+7000 m