2021
JEE Mains
Numerical
JEE Main 2021 (Online) 17th March Evening Shift
A boy of mass 4 kg is standing on a piece of wood having mass 5 kg. If the coefficient of friction between the wood and the floor is 0.5, the maximum force that the boy can exert on the rope so that the piece of wood does not move from its place is __________ N. (Round off to the Nearest Integer) [Take g = 10 ms-2 ]
Correct Answer: 30
Explanation:
$ \because $ f = T
$ \Rightarrow $ $\mu$N = T
$ \Rightarrow $ $\mu$(90 $-$ T) = T
$ \Rightarrow $ 0.5 (90 $-$ T) = T
$ \Rightarrow $ 90 $-$ T = 2T
$ \Rightarrow $ 3T = 90
$ \Rightarrow $ T = 30 N
2021
JEE Mains
Numerical
JEE Main 2021 (Online) 17th March Evening Shift
A body of mass 1 kg rests on a horizontal floor with which it has a coefficient of static friction ${1 \over {\sqrt 3 }}$. It is desired to make the body move by applying the minimum possible force F N. The value of F will be ____________. (Round off to the Nearest Integer) [Take g = 10 ms$-$2 ]
Correct Answer: 5
Explanation:
Minimum possible force $ \Rightarrow $
$F = {{\mu mg} \over {\sqrt {1 + {\mu ^2}} }}$
${F_{\min }} = {{{1 \over {\sqrt 3 }} \times 1 \times 10} \over {\sqrt {1 + {1 \over 3}} }}$
Fmin = 5N
2021
JEE Mains
Numerical
JEE Main 2021 (Online) 17th March Morning Shift
Two blocks (m = 0.5 kg and M = 4.5 kg) are arranged on a horizontal frictionless table as shown in figure. The coefficient of static friction between the two blocks is ${3 \over 7}$. Then the maximum horizontal force that can be applied on the larger block so that the blocks move together is ___________ N. (Round off to the Nearest Integer) [Take g as 9.8 ms$-$2]
Correct Answer: 21
Explanation:
$a = {F \over {M + m}}$
f = m$a$ = m${F \over {M + m}}$
m${F \over {M + m}}$ $ \le $ $\mu $mg (for no slipping)
$ \Rightarrow $ F $ \le $ $\mu $(m + M)g
$ \therefore $ Fmax = ${3 \over 7}\left( {0.5 + 4.5} \right) \times 9.8$ = 21 N
2021
JEE Mains
Numerical
JEE Main 2021 (Online) 16th March Evening Shift
A body of mass 2 kg moves under a force of $\left( {2\widehat i + 3\widehat j + 5\widehat k} \right)$N. It starts from rest and was at the origin initially. After 4s, its new coordinates are (8, b, 20). The value of b is _____________. (Round off to the Nearest Integer)
Correct Answer: 12
Explanation:
$\overrightarrow F = (2\widehat i + 3\widehat j + 5\widehat k)N$
time = 4 sec
As body start from rest therefore
position vector initially $\overrightarrow {{r_i}} = (0\widehat i + 0\widehat j + 0\widehat k)$ &
u (initial velocity) = 0
given, ${r_f} = (x\widehat i + y\widehat j + z\widehat k)$
Now, from second equation of motion
$\overrightarrow s = \overrightarrow u t + {1 \over 2}\overrightarrow a {t^2}$
${r_f} - {r_i} = {1 \over 2} \times \left( {{{2\widehat i + 3\widehat j + 5\widehat k} \over 2}} \right) \times {(4)^2}$
$ \Rightarrow $ $(x\widehat i + y\widehat j + z\widehat k) - (0\widehat i + 0\widehat j + 0\widehat k) = 8\widehat i + 12\widehat j + 20\widehat k$
$ \Rightarrow $ $x\widehat i + y\widehat j + z\widehat k = 8\widehat i + 12\widehat j + 20\widehat k$
$ \therefore $ The value of b = 12
time = 4 sec
As body start from rest therefore
position vector initially $\overrightarrow {{r_i}} = (0\widehat i + 0\widehat j + 0\widehat k)$ &
u (initial velocity) = 0
given, ${r_f} = (x\widehat i + y\widehat j + z\widehat k)$
Now, from second equation of motion
$\overrightarrow s = \overrightarrow u t + {1 \over 2}\overrightarrow a {t^2}$
${r_f} - {r_i} = {1 \over 2} \times \left( {{{2\widehat i + 3\widehat j + 5\widehat k} \over 2}} \right) \times {(4)^2}$
$ \Rightarrow $ $(x\widehat i + y\widehat j + z\widehat k) - (0\widehat i + 0\widehat j + 0\widehat k) = 8\widehat i + 12\widehat j + 20\widehat k$
$ \Rightarrow $ $x\widehat i + y\widehat j + z\widehat k = 8\widehat i + 12\widehat j + 20\widehat k$
$ \therefore $ The value of b = 12
2021
JEE Mains
Numerical
JEE Main 2021 (Online) 26th February Morning Shift
A person standing on a spring balance inside a stationary lift measures 60 kg. The weight of that person if the lift descends with uniform downward acceleration of 1.8 m/s2 will be ______________ N. [g = 10 m/s2]
Correct Answer: 492
Explanation:
The apparent weight $W_{\text{app}}$ of a person in an elevator moving with acceleration is given by:
$W_{\text{app}} = m(g - a)$
where:
- $W_{\text{app}}$ is the apparent weight,
- $m$ is the mass of the person,
- $g$ is the acceleration due to gravity,
- $a$ is the acceleration of the elevator.
Given that the person's mass is 60 kg, the acceleration due to gravity is 10 m/s², and the acceleration of the lift is 1.8 m/s², we can substitute these values into the formula:
$W_{\text{app}} = 60 \, \text{kg} \times (10 \, \text{m/s}^2 - 1.8 \, \text{m/s}^2) = 60 \, \text{kg} \times 8.2 \, \text{m/s}^2 = 492 \, \text{N}$
So, the apparent weight of the person when the lift descends with a uniform downward acceleration of 1.8 m/s² will be 492 N.
2021
JEE Mains
Numerical
JEE Main 2021 (Online) 26th February Morning Shift
A boy pushes a box of mass 2 kg with a force $\overrightarrow F = \left( {20\widehat i + 10\widehat j} \right)N$ on a frictionless surface. If the box was initially at rest, then ___________ m is displacement along the x-axis after 10s.
Correct Answer: 500
Explanation:
$\overrightarrow F = 20\widehat i + 10\widehat j$
$\overrightarrow a = {{\overrightarrow F } \over m} = {{20\widehat i + 10\widehat j} \over 2} = 10\widehat i + 5\widehat j$
$ \therefore $ $\overrightarrow s = {1 \over 2}\overrightarrow a {t^2} = {1 \over 2}\left( {10\widehat i + 5\widehat j} \right) \times {\left( {10} \right)^2}$
$ = 50\left( {10\widehat i + 5\widehat j} \right)m$
$ \therefore $ Displacement along x-axis
= 50 $\times$ 10 = 500 m
$\overrightarrow a = {{\overrightarrow F } \over m} = {{20\widehat i + 10\widehat j} \over 2} = 10\widehat i + 5\widehat j$
$ \therefore $ $\overrightarrow s = {1 \over 2}\overrightarrow a {t^2} = {1 \over 2}\left( {10\widehat i + 5\widehat j} \right) \times {\left( {10} \right)^2}$
$ = 50\left( {10\widehat i + 5\widehat j} \right)m$
$ \therefore $ Displacement along x-axis
= 50 $\times$ 10 = 500 m
2021
JEE Mains
Numerical
JEE Main 2021 (Online) 26th February Morning Shift
As shown in the figure, a block of mass $\sqrt 3 $ kg is kept on a horizontal rough surface of coefficient of friction ${1 \over {3\sqrt 3 }}$. The critical force to be applied on the vertical surface as shown at an angle 60$^\circ$ with horizontal such that it does not move, will be 3x. The value of x will be _________.
[g = 10 m/s2; sin60$^\circ$ = ${{\sqrt 3 } \over 2}$; cos60$^\circ$ = ${1 \over 2}$]
[g = 10 m/s2; sin60$^\circ$ = ${{\sqrt 3 } \over 2}$; cos60$^\circ$ = ${1 \over 2}$]
Correct Answer: 3.33
Explanation:
N = Mg + Fsin60$^\circ$
N = $\sqrt 3 g + {{F\sqrt 3 } \over 2}$
For No slipping
Fcos60$^\circ$ = Friction
${F \over 2} = \mu N = {1 \over {3\sqrt 3 }}\left( {\sqrt 3 g + {{F\sqrt 3 } \over 2}} \right)$
${F \over 2} = {g \over 3} + {F \over 6}$
${F \over 2} - {F \over 6} = {g \over 3}$
${{6F - 2F} \over {12}} = {g \over 3}$
4F = 4g
F = 10
F = 3x
x = ${F \over 3}$ = ${10 \over 3}$ = 3.33
x = 3.33
2021
JEE Mains
Numerical
JEE Main 2021 (Online) 24th February Morning Shift
An inclined plane is bent in such a way that the vertical cross-section is given by $y = {{{x^2}} \over 4}$ where y is in vertical and x in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction $\mu$ = 0.5, the maximum height in cm at which a stationary block will not slip downward is _________ cm.
Correct Answer: 25
Explanation:
The graph for given equation is shown below
At maximum height, the slope of tangent drawn,
$\tan \theta = {{dy} \over {dx}} = {{2x} \over 4} = {x \over 2}$ [$\because$ $y = {{{x^2}} \over 4}$]
$ \Rightarrow 0.5 = {x \over 2}$ ($\because$ $\mu$ = tan$\theta$)
$\Rightarrow$ x = 1 m
$\therefore$ $y = {{{x^2}} \over 4} = {1 \over 4}$ = 0.25 m = 25 cm
At maximum height, the slope of tangent drawn,
$\tan \theta = {{dy} \over {dx}} = {{2x} \over 4} = {x \over 2}$ [$\because$ $y = {{{x^2}} \over 4}$]
$ \Rightarrow 0.5 = {x \over 2}$ ($\because$ $\mu$ = tan$\theta$)
$\Rightarrow$ x = 1 m
$\therefore$ $y = {{{x^2}} \over 4} = {1 \over 4}$ = 0.25 m = 25 cm
2021
JEE Mains
Numerical
JEE Main 2021 (Online) 24th February Morning Shift
The coefficient of static friction between a wooden block of mass 0.5 kg and a vertical rough wall is 0.2. The magnitude of horizontal force that should be applied on the block to keep it adhere to the wall will be _________ N. [g = 10 ms$-$2]
Correct Answer: 25
Explanation:
Given, coefficient of static friction, $\mu$s = 0.2
Various forces acting on block are shown below
Frictional force $\le$ mg
$\Rightarrow$ N $\times$ 0.2 $\le$ 5
$\Rightarrow$ N $\le$ 25
$\therefore$ Magnitude of horizontal force, F = N = 25 N
Various forces acting on block are shown below
Frictional force $\le$ mg
$\Rightarrow$ N $\times$ 0.2 $\le$ 5
$\Rightarrow$ N $\le$ 25
$\therefore$ Magnitude of horizontal force, F = N = 25 N
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 6th September Evening Slot
A particle moving in the xy plane experiences a velocity dependent force
$\overrightarrow F = k\left( {{v_y}\widehat i + {v_x}\widehat j} \right)$ , where vx and vy are the
x and y components of its velocity $\overrightarrow v $ . If $\overrightarrow a $ is the
acceleration of the particle, then
which of the following statements is true for the particle?
$\overrightarrow F = k\left( {{v_y}\widehat i + {v_x}\widehat j} \right)$ , where vx and vy are the
x and y components of its velocity $\overrightarrow v $ . If $\overrightarrow a $ is the
acceleration of the particle, then
which of the following statements is true for the particle?
A.
kinetic energy of particle is constant in time
B.
quantity $\overrightarrow v \times \overrightarrow a $
is constant in time
C.
quantity $\overrightarrow v .\overrightarrow a $
is constant in time
D.
$\overrightarrow F $ arises due to a magnetic field
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 6th September Morning Slot
An insect is at the bottom of a hemispherical ditch of radius 1 m. It crawls up the ditch but starts
slipping after it is at height h from the bottom. If the coefficient of friction between the ground and
the insect is 0.75, then h is :
(g = 10 ms–2)
(g = 10 ms–2)
A.
0.45 m
B.
0.60 m
C.
0.20 m
D.
0.80 m
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 5th September Evening Slot
A spaceship in space sweeps stationary
interplanetary dust. As a result, its mass
increases at a rate ${{dM\left( t \right)} \over {dt}}$ = bv2(t), where v(t) is its instantaneous velocity. The instantaneous acceleration of the satellite is :
increases at a rate ${{dM\left( t \right)} \over {dt}}$ = bv2(t), where v(t) is its instantaneous velocity. The instantaneous acceleration of the satellite is :
A.
-bv3(t)
B.
$ - {{2b{v^3}} \over {M\left( t \right)}}$
C.
$ - {{b{v^3}} \over {M\left( t \right)}}$
D.
$ - {{b{v^3}} \over {2M\left( t \right)}}$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 4th September Evening Slot
A small ball of mass m is thrown upward with velocity u from the ground. The ball experiences a
resistive force mkv2
where v is its speed. The maximum height attained by the ball is :
A.
${1 \over k}{\tan ^{ - 1}}{{k{u^2}} \over {2g}}$
B.
${1 \over {2k}}{\tan ^{ - 1}}{{k{u^2}} \over g}$
C.
${1 \over {2k}}\ln \left( {1 + {{k{u^2}} \over g}} \right)$
D.
${1 \over k}\ln \left( {1 + {{k{u^2}} \over {2g}}} \right)$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 7th January Evening Slot
A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force F is applied
horizontally at the mid point of the rope such that the top half of the rope makes an angle of 45o
with the vertical. Then F equal : (Take g = 10 ms–2 and the rope to be massless)
A.
100 N
B.
75 N
C.
90 N
D.
70 N
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th April Evening Slot
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 30o 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 blocks, in case (B) and case (A) will be :
(g = 10 ms–2)
A.
3.2 ms–2
B.
0.8 ms–2
C.
0 ms–2
D.
0.4 ms–2
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th April Evening Slot
A spring whose unstretched length is l has a force constant k. The spring is cut into two pieces of unstretched
lengths l1 and l2 where, l1 = nl2 and n is an integer. The ratio k1/k2 of the corresponding force constant, k1 and
k2 will be :
A.
${1 \over {{n^2}}}$
B.
${1 \over n}$
C.
n2
D.
n
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th April Evening Slot
A bullet of mass 20 g has an initial speed of 1 ms–1
, just before it starts penetrating a mud wall of thickness
20 cm. If the wall offers a mean resistance of 2.5 × 10–2 N, the speed of the bullet after emerging from the
other side of the wall is close to :
A.
0.3 ms-1
B.
0.1 ms-1
C.
0.7 ms-1
D.
0.4 ms-1
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th April Evening Slot
Two blocks A and B of masses mA = 1 kg and mB = 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 m/s2]
[Take g = 10 m/s2]
A.
8 N
B.
16 N
C.
40 N
D.
12 N
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th April Morning Slot
A ball is thrown upward with an initial velocity
V0 from the surface of the earth. The motion
of the ball is affected by a drag force equal to
m$\gamma $u2 (where m is mass of the ball, u is its
instantaneous velocity and $\gamma $ is a constant).
Time taken by the ball to rise to its zenith is :
A.
${1 \over {\sqrt {\gamma g} }}{\tan ^{ - 1}}\left( {\sqrt {{\gamma \over g}} {V_0}} \right)$
B.
${1 \over {\sqrt {\gamma g} }}{ln}\left( 1+ {\sqrt {{\gamma \over g}} {V_0}} \right)$
C.
${1 \over {\sqrt {\gamma g} }}{\sin ^{ - 1}}\left( {\sqrt {{\gamma \over g}} {V_0}} \right)$
D.
${1 \over {\sqrt {2\gamma g} }}{\tan ^{ - 1}}\left( {\sqrt {{2\gamma \over g}} {V_0}} \right)$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 12th January Evening Slot
A block kept on a rough inclined plane, as shown in the figure, remains at rest upto a maximum force 2 N down the inclined plane. The maximum external force up the inclined plane that does not move the block is 10 N. The coefficient of static friction between the block and the plane is : [Take g = 10 m/s2]
A.
${{\sqrt 3 } \over 4}$
B.
${1 \over 2}$
C.
${{\sqrt 3 } \over 2}$
D.
${2 \over 3}$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th January Evening Slot
Two forces P and Q, of magnitude 2F and 3F, respectively, are at an angle $\theta $ with each other. If the force Q is doubled, then their resultant also gets doubled. Then, the angle $\theta $ is -
A.
90o
B.
60o
C.
30o
D.
120o
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th January Evening Slot
A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point. the rope deviated at an angle of 45o at the roof point. If the suspended mass is at equilibrium, the magnitude of the force applied is (g = 10 ms$-$2
A.
200 N
B.
140 N
C.
70 N
D.
100 N
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th January Morning Slot
A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force P, such that the block does not move downward? (take g = 10 ms$-$2)
A.
32 N
B.
18 N
C.
23 N
D.
25 N
2018
JEE Mains
MCQ
JEE Main 2018 (Offline)
Two masses m1 = 5 kg and m2 = 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 m2 to stop the motion is :
A.
10.3 kg
B.
18.3 kg
C.
27.3 kg
D.
43.3 kg
2018
JEE Mains
MCQ
JEE Main 2018 (Online) 15th April Evening Slot
A body of mass 2 kg slides down with an acceleration of 3 m/s2 on a rough inclined plane having a slope of ${30^o}$. The external force required to take the same body up the plane with the same acceleration will be : (g = 10 m/s2)
A.
14 N
B.
20 N
C.
6 N
D.
4 N
2018
JEE Mains
MCQ
JEE Main 2018 (Online) 15th April Morning Slot
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.
${1 \over {2 - {n^2}}}$
B.
$1 - {1 \over {{n^2}}}$
C.
$\sqrt {1 - {1 \over {{n^2}}}} $
D.
$\sqrt {{1 \over {1 - {n^2}}}} $
2016
JEE Mains
MCQ
JEE Main 2016 (Online) 10th April Morning Slot
A particle of mass m is acted upon by a force F given by the empirical law
F =${R \over {{t^2}}}\,v\left( t \right).$ If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot :
A.
$\upsilon $(t) against t2
B.
log $\upsilon $(t) against ${1 \over {{t^2}}}$
C.
log $\upsilon $(t) against t
D.
log $\upsilon $(t) against ${1 \over {{t}}}$
2016
JEE Mains
MCQ
JEE Main 2016 (Online) 9th April Morning Slot
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 $min between the mass and the inclined surface such that the mass does not move is :
A.
tan$\theta $
B.
2tan$\theta $
C.
3tan$\theta $
D.
tan2$\theta $
2015
JEE Mains
MCQ
JEE Main 2015 (Offline)
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.
$120$ $N$
B.
$150$ $N$
C.
$100$ $N$
D.
$80$ $N$
2014
JEE Mains
MCQ
JEE Main 2014 (Offline)
A block of mass $m$ is placed on a surface with a vertical cross section given by $y = {{{x^3}} \over 6}.$ 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.
${1 \over 6}m$
B.
${2 \over 3}m$
C.
${1 \over 3}m$
D.
${1 \over 2}m$
2012
JEE Mains
MCQ
AIEEE 2012
A particle of mass $m$ is at rest at the origin at time $t=0.$ It is subjected to a force $F\left( t \right) = {F_0}{e^{ - bt}}$ in the $x$ direction. Its speed $v(t)$ is depicted by which of the following curves?
A.
B.
C.
D.
2010
JEE Mains
MCQ
AIEEE 2010
Two fixed frictionless inclined planes making an angle ${30^ \circ }$ and ${60^ \circ }$ with the vertical are shown in the figure. Two blocks $A$ and $B$ are placed on the two planes. What is the relative vertical acceleration of $A$ with respect to $B$ ?
A.
$4.9m{s^{ - 2}}$ in horizontal direction
B.
$9.8m{s^{ - 2}}$ in vertical direction
C.
Zero
D.
$4.9m{s^{ - 2}}$ in vertical direction
2007
JEE Mains
MCQ
AIEEE 2007
A block of mass $m$ is connected to another block of $mass$ $M$ by a spring (massless) of spring constant $k.$ The block are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched. Then a constant force $F$ starts acting on the block of mass $M$ to pull it. Find the force of the block of mass $m.$
A.
${{MF} \over {\left( {m + M} \right)}}$
B.
${{mF} \over M}$
C.
${{\left( {M + m} \right)F} \over m}$
D.
${{mF} \over {\left( {m + M} \right)}}$
2005
JEE Mains
MCQ
AIEEE 2005
A particle of mass 0.3 kg subjected to a force $F=-kx$ with $k=15$ $N/m$. What will be its initial acceleration if it is released from a point 20 cm away from the origin?
A.
$15\,\,\,\,m/{s^2}$
B.
$3\,\,\,m/{s^2}$
C.
$10\,\,\,m/{s^2}$
D.
$5\,\,\,m/{s^2}$
2005
JEE Mains
MCQ
AIEEE 2005
A block is kept on a frictionless inclined surface with angle of inclination $'\,\alpha \,'.$ The incline is given an acceleration $a$ to keep the block stationary. Then $a$ is equal to
A.
$g$ $cosec$ $\alpha $
B.
$g/tan$ $\alpha $
C.
$g$ $tan$ $\alpha $
D.
$g$
2005
JEE Mains
MCQ
AIEEE 2005
Consider a car moving on a straight road with a speed of $100$ $m/s$. The distance at which car can be stopped is $\left[ {{\mu _k} = 0.5} \right]$
A.
$1000$ $m$
B.
$800$ $m$
C.
$400$ $m$
D.
$100$ $m$
2005
JEE Mains
MCQ
AIEEE 2005
A smooth block is released at rest on a ${45^ \circ }$ incline and then slides a distance $'d'$. The time taken to slide is $'n'$ times as much to slide on rough incline than on a smooth incline. The coefficient of friction is
A.
${\mu _k} = \sqrt {1 - {1 \over {{n^2}}}} $
B.
${\mu _k} = 1 - {1 \over {{n^2}}}$
C.
${\mu _k} = \sqrt {1 - {1 \over {{n^2}}}} $
D.
${\mu _s} = 1 - {1 \over {{n^2}}}$
2004
JEE Mains
MCQ
AIEEE 2004
Two masses ${m_1} = 5kg$ and ${m_2} = 4.8kg$ tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when left free to move? $\left( {g = 9.8m/{s^2}} \right)$
A.
$5\,\,m/{s^2}$
B.
$9.8\,\,m/{s^2}$
C.
$0.2\,\,m/{s^2}$
D.
$4.8\,\,m/{s^2}$
2004
JEE Mains
MCQ
AIEEE 2004
A block rests on a rough inclined plane `making an angle of ${30^ \circ }$ with the horizontal. The coefficient of static friction between the block and the plane is $0.8.$ If the frictionless force on the block is $10$ $N,$ the mass of the block (in $kg$) is $\left( {take\,\,\,g\, = \,10\,\,m/{s^2}} \right)$
A.
$1.6$
B.
$4.0$
C.
$2.0$
D.
$2.5$
2003
JEE Mains
MCQ
AIEEE 2003
A block of mass $M$ is pulled along a horizontal frictionless surface by a rope of mass $m.$ If a force $P$ is applied at the free end of the rope, the force exerted by the rope on the block is
A.
${{Pm} \over {M + m}}$
B.
${{Pm} \over {M - m}}$
C.
$P$
D.
${{PM} \over {M + m}}$
2003
JEE Mains
MCQ
AIEEE 2003
A horizontal force of $10$ $N$ is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is $0.2$. The weight of the block is
A.
$20N$
B.
$50N$
C.
$100N$
D.
$2N$
2003
JEE Mains
MCQ
AIEEE 2003
Three forces start acting simultaneously on a particle moving with velocity, $\overrightarrow v \,\,.$ These forces are represented in magnitude and direction by the three sides of a triangle $ABC$. The particle will now move with velocity
A.
less than $\overrightarrow v \,$
B.
greater than $\overrightarrow v \,$
C.
$\left| v \right|$ in the direction of the largest force $BC$
D.
$\overrightarrow v \,\,,$ remaining unchanged
2003
JEE Mains
MCQ
AIEEE 2003
A marble block of mass $2$ $kg$ lying on ice when given a velocity of $6$ $m/s$ is stopped by friction in $10$ $s.$ Then the coefficient of friction is
A.
$0.02$
B.
$0.03$
C.
$0.04$
D.
$0.06$
2003
JEE Mains
MCQ
AIEEE 2003
A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads $49$ $N,$ when the lift is stationary. If the lift moves downward with an acceleration of $5 m/{s^2}$, the reading of the spring balance will be
A.
$24$ $N$
B.
$74$ $N$
C.
$15$ $N$
D.
$49$ $N$
2003
JEE Mains
MCQ
AIEEE 2003
A light spring balance hangs from the hook of the other light spring balance and a block of mass $M$ $kg$ hangs from the former one. Then the true statement about the scale reading is
A.
Both the scales read $M$ $kg$ each
B.
The scale of the lower one reads $M$ $kg$ and of the upper one zero
C.
The reading of the two scales can be anything but the sum of the reading will be $M$ $kg$
D.
Both the scales read $M/2$ $kg$ each
2003
JEE Mains
MCQ
AIEEE 2003
A rocket with a lift-off mass $3.5 \times {10^4}\,\,kg$ is blasted upwards with an initial acceleration of $10m/{s^2}.$ Then the initial thrust of the blast is
A.
$3.5 \times {10^5}N$
B.
$7.0 \times {10^5}N$
C.
$14.0 \times {10^5}N$
D.
$1.75 \times {10^5}N$
2002
JEE Mains
MCQ
AIEEE 2002
A lift is moving down with acceleration $a.$ A man in the lift drops a ball inside the lift. The acceleration of the ball as observed by the man in the lift and a man standing stationary on the ground are respectively
A.
$g,g$
B.
$g-a, g-a$
C.
$g-a, g$
D.
$a, g$
2002
JEE Mains
MCQ
AIEEE 2002
A light string passing over a smooth light pulley connects two blocks of masses ${m_1}$ and ${m_2}$ (vertically). If the acceleration of the system is $g/8$, then the ratio of the masses is
A.
$8:1$
B.
$9:7$
C.
$4:3$
D.
$5:3$
2002
JEE Mains
MCQ
AIEEE 2002
Three identical blocks of masses $m=2$ $kg$ are drawn by a force $F=10.2$ $N$ with an acceleration of $0.6$ $m{s^{ - 2}}$ on a frictionless surface, then what is the tension (in $N$) in the string between the blocks $B$ and $C$?
A.
$9.2$
B.
$3.4$
C.
$4$
D.
$7.8$
Assume tension between block A and B is T1 and block B and C is T2. Acceleration a = 0.6 m/s2.
2002
JEE Mains
MCQ
AIEEE 2002
Two forces are such that the sum of their magnitudes is $18$ $N$ and their resultant is $12$ $N$ which is perpendicular to the smaller force. Then the magnitudes of the forces are
A.
$12N,$ $6N$
B.
$13N,$ $5N$
C.
$10N,$ $8N$
D.
$16N$, $2N.$
