JEE (Main) April 2019
Q101
Errorless
14. Critical Thinking-friction
MCQ
A block of mass 5 kg is (i) pushed in case (A) and (ii) pulled in case (B), by a force F=20 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: $(g=10\ ms^{-2})$
(A)
(B)
(A)
(B)
A.
$0ms^{-2}$
B.
$0.8ms^{-2}$
C.
$0.4ms^{-2}$
D.
$3.2ms^{-2}$
JEE (Main) 2018
Q102
Errorless
4. 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
Q103
Errorless
9. 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 $e^{-1} = 0.37$
Correct Answer: 6.30
Explanation:
$J = 1 \longrightarrow \boxed {m = 0. 4}$
$v = v _ {0} e ^ {- t / \tau}$
$v _ {0} = \frac {J}{m} = 2. 5 m / s$
$v = v _ {0} e ^ {- t / \tau} \Rightarrow \frac {d x}{d t} = v _ {0} e ^ {- t / \tau}$
$\int_ {0} ^ {x} d x = v _ {0} \int_ {0} ^ {\tau} e ^ {- t / \tau} d t$
$\int e ^ {- x} d x = \frac {e ^ {- x}}{- 1}$
$x = v _ {0} \left[ \frac {e ^ {- t / \tau}}{- \frac {1}{\tau}} \right] _ {0} ^ {\tau}$
$x = 2.5 (- 4) (e ^ {- 1} - e ^ {0}) \Rightarrow x = 6.3 0.$
$v = v _ {0} e ^ {- t / \tau}$
$v _ {0} = \frac {J}{m} = 2. 5 m / s$
$v = v _ {0} e ^ {- t / \tau} \Rightarrow \frac {d x}{d t} = v _ {0} e ^ {- t / \tau}$
$\int_ {0} ^ {x} d x = v _ {0} \int_ {0} ^ {\tau} e ^ {- t / \tau} d t$
$\int e ^ {- x} d x = \frac {e ^ {- x}}{- 1}$
$x = v _ {0} \left[ \frac {e ^ {- t / \tau}}{- \frac {1}{\tau}} \right] _ {0} ^ {\tau}$
$x = 2.5 (- 4) (e ^ {- 1} - e ^ {0}) \Rightarrow x = 6.3 0.$
NEET 2018
Q104
Errorless
12. 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
WB-JEE 2016
Q105
Errorless
4. 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
Q106
Errorless
4. 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
Q107
Errorless
11. 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
Q108
Errorless
13. 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
Q109
Errorless
14. 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.
$\frac{h}{\ell}=\frac{3\sqrt{3}}{16}, f=\frac{16\sqrt{3}}{3}N$
WB-JEE 2015
Q110
Errorless
11. 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
Q111
Errorless
11. 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
Q112
Errorless
13. 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
CBSE PMT 2014
Q113
Errorless
2. 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
Q114
Errorless
8. 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
Q115
Errorless
10. 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-I | Column-II | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
Correct Answer: A → p; B → p; C → p; D → s
Explanation:
$\mathbf{A} \rightarrow \mathbf{p}; \mathbf{B} \rightarrow \mathbf{p}; \mathbf{C} \rightarrow \mathbf{p}; \mathbf{D} \rightarrow \mathbf{s}$
Match the column
When lift is at rest:
$d = \sqrt {4 h _ {1} h _ {2}}$
A) $g_{eff} > g$ $d = \sqrt{4h_1h_2} = 1.2m$
B) $g_{eff} < g$ $d = \sqrt{4h_1h_2} = 1.2m$
C) $g_{eff} = g$ $d = \sqrt{4h_1h_2} = 1.2m$
D) $g_{eff} = 0$ No water leaks out of the jar.
Match the column
When lift is at rest:
$d = \sqrt {4 h _ {1} h _ {2}}$
A) $g_{eff} > g$ $d = \sqrt{4h_1h_2} = 1.2m$
B) $g_{eff} < g$ $d = \sqrt{4h_1h_2} = 1.2m$
C) $g_{eff} = g$ $d = \sqrt{4h_1h_2} = 1.2m$
D) $g_{eff} = 0$ No water leaks out of the jar.
CBSE PMT 2014
Q116
Errorless
11. 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
Q117
Errorless
19. 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 : $\tan(5.5^{\circ})\approx0.1;\tan(11.5^{\circ})\approx0.2;$
$\tan (16.5^{\circ}\approx 0.3)]$
[Useful information : $\tan(5.5^{\circ})\approx0.1;\tan(11.5^{\circ})\approx0.2;$
$\tan (16.5^{\circ}\approx 0.3)]$
| Column-I | Column-II | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
|
Correct Answer: 6.30
Explanation:
$\mathbf{A}\rightarrow \mathbf{q};\mathbf{B}\rightarrow \mathbf{q};\mathbf{C}\rightarrow \mathbf{r};\mathbf{D}\rightarrow \mathbf{r}$
Block will not slip if
$(m_{1} + m_{2})g\sin \theta \leq \mu m_{2}g\cos \theta$
$3\sin \theta \leq \left(\frac{3}{10}\right)(2)\cos \theta$
$\tan \theta \leq \frac {1}{5} \Rightarrow \theta \leq 11.5 ^ {\circ}$
A) $\theta = 5^{\circ}$ friction is static $f = (m_{1} + m_{2})g\sin \theta$
B) $\theta = 10^{\circ}$ friction is static $f = (m_{1} + m_{2})g\sin \theta$
C) $\theta = 15^{\circ}$ friction is kinetic $f = \mu m_{2}g\cos \theta$
D) $\theta = 20^{\circ}$ friction is kinetic $f = \mu m_{2}g\cos \theta$
Block will not slip if
$(m_{1} + m_{2})g\sin \theta \leq \mu m_{2}g\cos \theta$
$3\sin \theta \leq \left(\frac{3}{10}\right)(2)\cos \theta$
$\tan \theta \leq \frac {1}{5} \Rightarrow \theta \leq 11.5 ^ {\circ}$
A) $\theta = 5^{\circ}$ friction is static $f = (m_{1} + m_{2})g\sin \theta$
B) $\theta = 10^{\circ}$ friction is static $f = (m_{1} + m_{2})g\sin \theta$
C) $\theta = 15^{\circ}$ friction is kinetic $f = \mu m_{2}g\cos \theta$
D) $\theta = 20^{\circ}$ friction is kinetic $f = \mu m_{2}g\cos \theta$
WB-JEE 2013
Q118
Errorless
4. 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
Q119
Errorless
6. 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
Q120
Errorless
9. 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
Q121
Errorless
13. 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
Q122
Errorless
2. 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
Kerala PET 2012
Q123
Errorless
5. Equilibrium of Forces
MCQ
The sum of magnitudes of two forces acting at a point is 16 N and their resultant $8\sqrt{3}$ N is at $90^{\circ}$ with the force of smaller magnitude. The two forces (in N) are
A.
11, 5
B.
9, 7
C.
6, 10
D.
4, 12
E.
2, 14
WB-JEE 2012; AIPMT (Cancelled) 2015
Q124
Errorless
6. Motion of Connected Bodies
MCQ
Three blocks A, B and C of masses 4 kg, 2 kg and 1 kg respectively, are in contact on a frictionless surface, as shown. If a force of 14 N is applied on the 4 kg block then the contact force between A and B is
A.
6N
B.
8N
C.
18N
D.
2N
J & K CET 2012
Q125
Errorless
6. Motion of Connected Bodies
MCQ
Two blocks, of mass 1 kg and 2 kg respectively, are connected by a spring and kept on a frictionless table. The blocks are pulled apart, so that the spring is stretched, and released from rest. At a certain instant of time, the block of mass 1 kg, is found to be moving at a speed 2 m/s. What must be the speed of the other block at this instant
A.
1 m/s
B.
0.5 m/s
C.
4 m/s
D.
0.25 m/s
