Work Power & Energy
155 Questions
2021
JEE Mains
Numerical
JEE Main 2021 (Online) 18th March Morning Shift
As shown in the figure, a particle of mass 10 kg is placed at a point A. When the particle is slightly displaced to its right, it starts moving and reaches the point B. The speed of the particle at B is x m/s. (Take g = 10 m/s2)
The value of 'x' to the nearest integer is __________.
The value of 'x' to the nearest integer is __________.
Correct Answer: 10
Explanation:
By energy conservation
Ki + Ui = Kf + Uf
0 + 10 $\times$ 10 $\times$ 10 = ${1 \over 2}$ $\times$ 10 $\times$ v$_B^2$ + 10 $\times$ 10 $\times$ 5
1000 = 5v$_B^2$ + 500
v$_B^2$ = ${{500} \over 5}$ = 100
VB = 10 m/s
x = 10
Ki + Ui = Kf + Uf
0 + 10 $\times$ 10 $\times$ 10 = ${1 \over 2}$ $\times$ 10 $\times$ v$_B^2$ + 10 $\times$ 10 $\times$ 5
1000 = 5v$_B^2$ + 500
v$_B^2$ = ${{500} \over 5}$ = 100
VB = 10 m/s
x = 10
2021
JEE Mains
Numerical
JEE Main 2021 (Online) 25th February Morning Shift
The potential energy (U) of a diatomic molecule is a function dependent on r (interatomic distance) as
$U = {\alpha \over {{r^{10}}}} - {\beta \over {{r^5}}} - 3$
where, $\alpha$ and $\beta$ are positive constants. The equilibrium distance between two atoms will be ${\left( {{{2\alpha } \over \beta }} \right)^{{a \over b}}}$, where a = ___________.
$U = {\alpha \over {{r^{10}}}} - {\beta \over {{r^5}}} - 3$
where, $\alpha$ and $\beta$ are positive constants. The equilibrium distance between two atoms will be ${\left( {{{2\alpha } \over \beta }} \right)^{{a \over b}}}$, where a = ___________.
Correct Answer: 1
Explanation:
$F = - {{dU} \over {dr}}$
$F = - \left[ { - {{10\alpha } \over {{r^{11}}}} + {{5\beta } \over {{r^6}}}} \right]$
for equilibrium, F = 0
${{10\alpha } \over {{r^{11}}}} = {{5\beta } \over {{r^6}}}$
${{2\alpha } \over \beta } = {r^5}$
$r = {\left( {{{2\alpha } \over \beta }} \right)^{1/5}}$
$ \therefore $ $a = 1$
$F = - \left[ { - {{10\alpha } \over {{r^{11}}}} + {{5\beta } \over {{r^6}}}} \right]$
for equilibrium, F = 0
${{10\alpha } \over {{r^{11}}}} = {{5\beta } \over {{r^6}}}$
${{2\alpha } \over \beta } = {r^5}$
$r = {\left( {{{2\alpha } \over \beta }} \right)^{1/5}}$
$ \therefore $ $a = 1$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 6th September Morning Slot
If the potential energy between two molecules is given by
U = $ - {A \over {{r^6}}} + {B \over {{r^{12}}}}$,
then at equilibrium, separation between molecules, and the potential energy are :
U = $ - {A \over {{r^6}}} + {B \over {{r^{12}}}}$,
then at equilibrium, separation between molecules, and the potential energy are :
A.
${\left( {{{2B} \over A}} \right)^{1/6}}$, $ - {{{A^2}} \over {4B}}$
B.
${\left( {{{2B} \over A}} \right)^{1/6}}, - {{{A^2}} \over {2B}}$
C.
${\left( {{B \over A}} \right)^{1/6}},0$
D.
${\left( {{B \over {2A}}} \right)^{1/6}}, - {{{A^2}} \over {2B}}$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 4th September Evening Slot
A person pushes a box on a rough horizontal plateform surface. He applies a force of 200 N over a
distance of 15 m. Thereafter, he gets progressively tired and his applied force reduces linearly with
distance to 100 N. The total distance through which the box has been moved is 30 m. What is the
work done by the person during the total movement of the box?
A.
5690 J
B.
5250 J
C.
2780 J
D.
3280 J
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 3rd September Evening Slot
A particle is moving unidirectionally on a horizontal plane under the action of a constant power
supplying energy source. The displacement (s) - time (t) graph that describes the motion of the
particle is (graphs are drawn schematically and are not to scale) :
A.
B.
C.
D.
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 9th January Morning Slot
Consider a force $\overrightarrow F = - x\widehat i + y\widehat j$
. The work done
by this force in moving a particle from point
A(1, 0) to B(0, 1) along the line segment is :
(all quantities are in SI units)
A.
2
B.
${1 \over 2}$
C.
1
D.
${3 \over 2}$
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 7th January Evening Slot
An elevator in a building can carry a maximum of 10 persons, with the average mass of each
person being 68 kg, The mass of the elevator itself is 920 kg and it moves with a constant speed
of 3 m/s. The frictional force opposing the motion is 6000 N. If the elevator is moving up with its
full capacity, the power delivered by the motor to the elevator (g = 10 m/s2) must be at least :
A.
48000 W
B.
62360 W
C.
56300 W
D.
66000 W
2020
JEE Mains
MCQ
JEE Main 2020 (Online) 7th January Morning Slot
A 60 HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg. If the frictional force on the elevator is 4000 N, the speed of the elevator at full load is close to :
(1 HP = 746 W, g = 10 ms-2)
(1 HP = 746 W, g = 10 ms-2)
A.
1.5 ms-1
B.
1.7 ms-1
C.
2.0 ms-1
D.
1.9 ms-1
2020
JEE Mains
Numerical
JEE Main 2020 (Online) 5th September Evening Slot
A body of mass 2 kg is driven by an engine
delivering a constant power of 1 J/s. The body
starts from rest and moves in a straight line.
After 9 seconds, the body has moved a
distance (in m) _______.
Correct Answer: 18
Explanation:
Let s be the required distance.
From Work - Energy theorem,
Work = Change in kinetic energy
$\Rightarrow$ Power $\times$ Time = $\Delta$K
i.e., Pt = $\Delta$K $\Rightarrow$ Pt = ${1 \over 2}$mv2 ..... (i)
Given, P = 1 Js$-$1, t = 9 s, m = 2 kg
Substituting all the given values in eq. (i), we get
1 $\times$ 9 = ${1 \over 2}$(2) v2
v2 = 9 $\Rightarrow$ v = 3 m/s (at t = 9 s)
As, Fv = P $\Rightarrow$ (ma)v = P [$\because$ F = ma]
$ \Rightarrow m\left[ {{{dv} \over {dt}}} \right]v = P \Rightarrow m\left[ {{{ds} \over {dt}}{{dv} \over {ds}}} \right]v = P$
$ \Rightarrow m\left[ {v{{dv} \over {ds}}} \right]v = P$
$ \Rightarrow 2{v^2}dv = ds$ {$\because$ P = 1 J/s and m = 2 kg}
Integrating both sides,
$\int\limits_0^3 {2{v^2}dv = \int\limits_0^s {ds \Rightarrow {2 \over 3}[{v^3}]_0^3 = 8} } $
${2 \over 3}[27 - 0] = s \Rightarrow s = 18$ m
Hence, after 9 s, the body has moved a distance of 18 m.
2020
JEE Mains
Numerical
JEE Main 2020 (Online) 3rd September Evening Slot
A block starts moving up an inclined plane of inclination 30o with an initial velocity of v0
. It comes
back to its initial position with velocity ${{{v_0}} \over 2}$. The value of the coefficient of kinetic friction between
the block and the inclined plane is close to ${I \over {1000}}$. The nearest integer to I is____.
Correct Answer: 346
Explanation:
a = g sin 30 + $\mu $ g cos 30
We know, v2 = u2 + 2as
$ \Rightarrow $ 0 = $v_0^2$ - 2ad
$ \Rightarrow $ $v_0^2 = 2ad$
$d = {{v_0^2} \over {2a}}$
Total work done,
${W_f} = {k_f} - {k_i}$
$ \Rightarrow $ $ - 2\mu mg\,\cos 30{{v_0^2} \over {2a}} = {1 \over 2}m{{v_0^2} \over 4} - {1 \over 2}mv_0^2$
$ \Rightarrow $ ${{ + \mu g\,\cos 30} \over a} = $${3 \over 8}$
$ \Rightarrow $ $8\mu g\,\cos 30 = 3g\,\sin 30 + 3\mu \,\cos 30$
$ \Rightarrow $ $5\mu g\,\cos 30 = 3g\,\sin 30$
$ \Rightarrow $ $\mu = {{3\tan 30} \over 5} = {{\sqrt 3 } \over 5}$
$ \Rightarrow $ ${{\sqrt 3 } \over 5} = {I \over {1000}}$
$ \Rightarrow $ $I = 346$
2020
JEE Mains
Numerical
JEE Main 2020 (Online) 3rd September Morning Slot
A cricket ball of mass 0.15 kg is thrown
vertically up by a bowling machine so that it
rises to a maximum height of 20 m after leaving
the machine. If the part pushing the ball applies
a constant force F on the ball and moves
horizontally a distance of 0.2 m while launching
the ball, the value of F (in N) is (g = 10 ms–2)
____.
Correct Answer: 150
Explanation:
Initial velocity, v = $\sqrt {2gh} $
= $\sqrt {2 \times 10 \times 20} $
= 20 m/s
Now work done by the machine,
WF = $\Delta $k
$ \Rightarrow $ F.d = $\Delta $k
$ \Rightarrow $ F = ${{\Delta k} \over d}$
= ${{{1 \over 2} \times 0.15 \times 400 - 0} \over {0.2}}$
= 150 N
= $\sqrt {2 \times 10 \times 20} $
= 20 m/s
Now work done by the machine,
WF = $\Delta $k
$ \Rightarrow $ F.d = $\Delta $k
$ \Rightarrow $ F = ${{\Delta k} \over d}$
= ${{{1 \over 2} \times 0.15 \times 400 - 0} \over {0.2}}$
= 150 N
2020
JEE Mains
Numerical
JEE Main 2020 (Online) 2nd September Morning Slot
A small block starts slipping down from a point B on an inclined plane AB, which is making an angle $\theta $ with the horizontal section BC is smooth and the remaining section CA is rough with a coefficient of friction $\mu $. It is found that the block comes to rest as it reaches the bottom (point A) of the inclined plane. If BC = 2AC, the coefficient of friction is given by $\mu $ = ktan $\theta $ . The value of k is _________.
Correct Answer: 3
Explanation:
Apply work energy theorem
Wg + Wf = $\Delta $kE
mgsin$\theta $ (AC + 2AC) – $\mu $mg cos$\theta $ $ \times $ AC = 0 - 0
$ \Rightarrow $ $\mu $ = 3tan $\theta $
2020
JEE Mains
Numerical
JEE Main 2020 (Online) 7th January Morning Slot
A particle (m = 1 kg) slides down a frictionless track (AOC) starting from rest at a point A (height 2 m). After reaching C, the particle continues to move freely in air as a projectile. When it reaching its highest point P (height 1 m), the kinetic energy of the particle (in )) is :
(Figure drawn is schematic and not to scale; take g = 10 ms-2)
(Figure drawn is schematic and not to scale; take g = 10 ms-2)
Correct Answer: 10
Explanation:
KE = PE1 – PE2 = mgh1 – mgh2
= 1 × 10 × 2 – 1 × 10 × 1 = 10 J
= 1 × 10 × 2 – 1 × 10 × 1 = 10 J
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th April Morning Slot
A uniform cable of mass 'M' and length 'L' is
placed on a horizontal surface such that its (1/n)th
part is hanging below the edge of the
surface. To lift the hanging part of the cable upto
the surface, the work done should be :
A.
${{2MgL} \over {{n^2}}}$
B.
nMgL
C.
${{MgL} \over {2{n^2}}}$
D.
${{MgL} \over {{n^2}}}$
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 8th April Morning Slot
A particle moves in one dimension from rest
under the influence of a force that varies with
the distance travelled by the particle as shown
in the figure. The kinetic energy of the particle
after it has travelled 3m is :
A.
6.5 J
B.
2.5 J
C.
5 J
D.
4 J
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th January Evening Slot
A particle which is experiencing a force, given by $\overrightarrow F = 3\widehat i - 12\widehat j,$ undergoes a displacement of $\overrightarrow d = 4\overrightarrow i $ particle had a kinetic energy of 3 J at the beginning of the displacement, what is its kinetic energy at the end of the displacement ?
A.
9 J
B.
10 J
C.
12 J
D.
15 J
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 10th January Morning Slot
A block of mass m is kept on a platform which starts from rest with constant acceleration g/2 upward, as shown in figure. Work done by normal reaction on block in time is -
A.
${{m{g^2}{t^2}} \over 8}$
B.
${{3m{g^2}{t^2}} \over 8}$
C.
$-$ ${{m{g^2}{t^2}} \over 8}$
D.
0
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th January Evening Slot
A force acts on a 2 kg object so that its position is given as a function of time as x = 3t2 + 5. What is the work done by this force in first 5 seconds ?
A.
850 J
B.
950 J
C.
875 J
D.
900 J
2019
JEE Mains
MCQ
JEE Main 2019 (Online) 9th January Morning Slot
A block of mass m, lying on a smooth horizontal surface, is attached to a sring (of negligible mass) of spring constant k. The other end of the spring is fixed, as shown in the figure. The block is initially at rest in its equilibrium position. If now the block is pulled with a constant force F, the maximum speed of the block is :
A.
${{2F} \over {\sqrt {mk} }}$
B.
${F \over {\pi \sqrt {mk} }}$
C.
${{\pi F} \over {\sqrt {mk} }}$
D.
${F \over {\sqrt {mk} }}$
2018
JEE Mains
MCQ
JEE Main 2018 (Online) 16th April Morning Slot
Two particles of the same mass m are moving in circular orbits because of force, given by $F\left( r \right) = {{ - 16} \over r} - {r^3}$
The first particle is at a distance r = 1, and the second, at r = 4. The best estimate for the ratio of kinetic energies of the first and the second particle is closest to :
The first particle is at a distance r = 1, and the second, at r = 4. The best estimate for the ratio of kinetic energies of the first and the second particle is closest to :
A.
$6 \times {10^{ - 2}}$
B.
$3 \times {10^{ - 3}}$
C.
${10^{ - 1}}$
D.
$6 \times {10^{ 2}}$
2018
JEE Mains
MCQ
JEE Main 2018 (Online) 16th April Morning Slot
A body of mass m starts moving from rest along x-axis so that its velocity varies as $\upsilon = a\sqrt s $ where a is a constant and s is the distance covered by the body. The total work done by all the forces acting on the body in the first t seconds after the start of the motion is :
A.
${1 \over 8}\,$ m a4 t2
B.
8 m a4 t2
C.
4 m a4 t2
D.
${1 \over 4}\,$ m a4 t2
2018
JEE Mains
MCQ
JEE Main 2018 (Offline)
A particle is moving in a circular path of radius $a$ under the action of an attractive potential $U = - {k \over {2{r^2}}}$ Its total energy is:
A.
$ - {3 \over 2}{k \over {{a^2}}}$
B.
Zero
C.
$ - {k \over {4{a^2}}}$
D.
$ {k \over {2{a^2}}}$
2017
JEE Mains
MCQ
JEE Main 2017 (Online) 8th April Morning Slot
An object is dropped from a height h from the ground. Every time it hits the ground it looses 50% of its kinetic energy. The total distance covered as t $ \to $ $\infty $ is :
A.
3h
B.
$\infty $
C.
${5 \over 3}$h
D.
${8 \over 3}$h
2017
JEE Mains
MCQ
JEE Main 2017 (Offline)
A time dependent force F = 6t acts on a particle of mass 1 kg. If the particle starts from rest, the work done
by the force during the first 1 sec. will be:
A.
18 J
B.
4.5 J
C.
22 J
D.
9 J
2017
JEE Mains
MCQ
JEE Main 2017 (Offline)
A body of mass m = 10–2 kg is moving in a medium and experiences a frictional force F = –kv2. Its initial speed is v0 = 10 ms–1. If, after 10 s, its energy is ${1 \over 8}mv_0^2$, the value of k will be:
A.
10-1 kg m-1 s-1
B.
10-3 kg m-1
C.
10-3 kg s-1
D.
10-4 kg m-1
2016
JEE Mains
MCQ
JEE Main 2016 (Online) 10th April Morning Slot
Velocity-time graph for a body of mass 10 kg is shown in figure. Work-done on
the body in first two seconds of the motion is :
A.
12000 J
B.
$-$ 12000 J
C.
$-$ 4500 J
D.
$-$ 9300 J
2016
JEE Mains
MCQ
JEE Main 2016 (Online) 10th April Morning Slot
A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at time t is given by n2 R t2 where n is a constant. The power delivered to the particle by the force acting on it, is :
A.
M n2 R2 t
B.
M n R2 t
C.
M n R2 t2
D.
${1 \over 2}$ M n2 R2 t2
2016
JEE Mains
MCQ
JEE Main 2016 (Online) 9th April Morning Slot
A car of weight W is on an inclined road that rises by 100 m over a distance of 1 km
and applies a constant frictional force ${W \over 20}$ on the car. While moving uphill on the road at a speed of 10 ms−1, the car needs power P. If it needs power ${p \over 2}$ while moving downhill at speed v then value of $\upsilon $ is :
A.
20 ms$-$1
B.
15 ms$-$1
C.
10 ms$-$1
D.
5 ms$-$1
2016
JEE Mains
MCQ
JEE Main 2016 (Offline)
A point particle of mass $m,$ moves long the uniformly rough track $PQR$ as shown in the figure. The coefficient of friction, between the particle and the rough track equals $\mu .$ The particle is released, from rest from the point $P$ and it comes to rest at point $R.$ The energies, lost by the ball, over the parts, $PQ$ and $QR$, of the track, are equal to each other , and no energy is lost when particle changes direction from $PQ$ to $QR$.
The value of the coefficient of friction $\mu $ and the distance $x$ $(=QR),$ are, respectively close to:
A.
$0.29$ and $3.5$ $m$
B.
$0.29$ and $6.5$ $m$
C.
$0.2$ and $6.5$ $m$
D.
$0.2$ and $3.5$ $m$
2016
JEE Mains
MCQ
JEE Main 2016 (Offline)
A person trying to lose weight by burning fat lifts a mass of $10$ $kg$ upto a height of $1$ $m$ $1000$ times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies $3.8 \times {10^7}J$ of energy per $kg$ which is converted to mechanical energy with a $20\% $ efficiency rate. Take $g = 9.8\,m{s^{ - 2}}$ :
A.
$9.89 \times {10^{ - 3}}\,\,kg$
B.
$12.89 \times {10^{ - 3}}\,kg$
C.
$2.45 \times {10^{ - 3}}\,\,kg$
D.
$6.45 \times {10^{ - 3}}\,\,kg$
2014
JEE Mains
MCQ
JEE Main 2014 (Offline)
When a rubber-band is stretched by a distance $x$, it exerts restoring force of magnitude $F = ax + b{x^2}$ where $a$ and $b$ are constants. The work done in stretching the unstretched rubber-band by $L$ is :
A.
$a{L^2} + b{L^3}$
B.
${1 \over 2}\left( {a{L^2} + b{L^3}} \right)$
C.
${{a{L^2}} \over 2} + {{b{L^3}} \over 3}$
D.
${1 \over 2}\left( {{{a{L^2}} \over 2} + {{b{L^3}} \over 3}} \right)$
2012
JEE Mains
MCQ
AIEEE 2012
This question has Statement $1$ and Statement $2.$ Of the four choices given after the Statements, choose the one that best describes the two Statements.
If two springs ${S_1}$ and ${S_2}$ of force constants ${k_1}$ and ${k_2}$, respectively, are stretched by the same force, it is found that more work is done on spring ${S_1}$ than on spring ${S_2}$.
STATEMENT 1: If stretched by the same amount work done on ${S_1}$, Work done on ${S_1}$ is more than ${S_2}$
STATEMENT 2: ${k_1} < {k_2}$
A.
Statement 1 is false, Statement 2 is true
B.
Statement 1 is true, Statement 2 is false
C.
Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation for Statement 1
D.
Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1
2010
JEE Mains
MCQ
AIEEE 2010
The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U\left( x \right) = {a \over {{x^{12}}}} - {b \over {{x^6}}},$ where $a$ and $b$ are constants and $x$ is the distance between the atoms. If the dissociation energy of the molecule is $D = \left[ {U\left( {x = \infty } \right) - {U_{at\,\,equilibrium}}} \right],\,\,D$ is
A.
${{{b^2}} \over {2a}}$
B.
${{{b^2}} \over {12a}}$
C.
${{{b^2}} \over {4a}}$
D.
${{{b^2}} \over {6a}}$
2008
JEE Mains
MCQ
AIEEE 2008
An athlete in the olympic games covers a distance of $100$ $m$ in $10$ $s.$ His kinetic energy can be estimated to be in the range
A.
$200J-500J$
B.
$2 \times {10^5}J - 3 \times {10^5}J$
C.
$20,000J - 50,000J$
D.
$2,000J - 5,000J$
2007
JEE Mains
MCQ
AIEEE 2007
A $2$ $kg$ block slides on a horizontal floor with a speed of $4m/s.$ It strikes a uncompressed spring, and compress it till the block is motionless. The kinetic friction force is $15N$ and spring constant is $10, 000$ $N/m.$ The spring compresses by
A.
$8.5cm$
B.
$5.5cm$
C.
$2.5cm$
D.
$11.0cm$
2007
JEE Mains
MCQ
AIEEE 2007
A particle is projected at $60^\circ $ to the horizontal with a kinetic energy K. The kinetic energy at the
highest point is
A.
K/2
B.
K
C.
Zero
D.
K/4
2006
JEE Mains
MCQ
AIEEE 2006
The potential energy of a $1$ $kg$ particle free to move along the $x$-axis is given by $V\left( x \right) = \left( {{{{x^4}} \over 4} - {{{x^2}} \over 2}} \right)J$.
The total mechanical energy of the particle is $2J.$ Then, the maximum speed (in $m/s$) is
A.
${3 \over {\sqrt 2 }}$
B.
${\sqrt 2 }$
C.
${1 \over {\sqrt 2 }}$
D.
$2$
2006
JEE Mains
MCQ
AIEEE 2006
A ball of mass $0.2$ $kg$ is thrown vertically upwards by applying a force by hand. If the hand moves $0.2$ $m$ while applying the force and the ball goes upto $2$ $m$ height further, find the magnitude of the force. (consider $g = 10\,m/{s^2}$).
A.
$4N$
B.
$16$ $N$
C.
$20$ $N$
D.
$22$ $N$
2006
JEE Mains
MCQ
AIEEE 2006
A particle of mass $100g$ is thrown vertically upwards with a speed of $5$ $m/s$. The work done by the force of gravity during the time the particle goes up is
A.
$-0.5J$
B.
$-1.25J$
C.
$1.25J$
D.
$0.5J$
2006
JEE Mains
MCQ
AIEEE 2006
A mass of $M$ $kg$ is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle of ${45^ \circ }$ with the initial vertical direction is
A.
$Mg\left( {\sqrt 2 + 1} \right)$
B.
$Mg\sqrt 2 $
C.
${{Mg} \over {\sqrt 2 }}$
D.
$Mg\left( {\sqrt 2 - 1} \right)$
From work energy theorem we can say,
2005
JEE Mains
MCQ
AIEEE 2005
A bullet fired into a fixed target loses half of its velocity after penetrating $3$ $cm.$ How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?
A.
$2.0$ $cm$
B.
$3.0$ $cm$
C.
$1.0$ $cm$
D.
$1.5$ $cm$
2005
JEE Mains
MCQ
AIEEE 2005
A spherical ball of mass $20$ $kg$ is stationary at the top of a hill of height $100$ $m$. It rolls down a smooth surface to the ground, then climbs up another hill of height $30$ $m$ and finally rolls down to a horizontal base at a height of $20$ $m$ above the ground. The velocity attained by the ball is
A.
$20$ $m/s$
B.
$40$ $m/s$
C.
$10\sqrt {30} \,\,\,m/s$
D.
$10\,\,m/s$
2005
JEE Mains
MCQ
AIEEE 2005
A body of mass $m$ is accelerated uniformly from rest to a speed $v$ in a time $T.$ The instantaneous power delivered to the body as a function of time is given by
A.
${{m{v^2}} \over {{T^2}}}.{t^2}$
B.
${{m{v^2}} \over {{T^2}}}.t$
C.
${1 \over 2}{{m{v^2}} \over {{T^2}}}.{t^2}$
D.
${1 \over 2}{{m{v^2}} \over {{T^2}}}.t$
2005
JEE Mains
MCQ
AIEEE 2005
The upper half of an inclined plane with inclination $\phi $ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by
A.
$2\,\cos \,\,\phi $
B.
$2\,sin\,\,\phi $
C.
$\,\tan \,\,\phi $
D.
$2\,\tan \,\,\phi $
2004
JEE Mains
MCQ
AIEEE 2004
A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to
A.
$x$
B.
${e^x}$
C.
${x^2}$
D.
${\log _e}x$
2004
JEE Mains
MCQ
AIEEE 2004
A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle, the motion of the particles takes place in a plane. It follows that
A.
its kinetic energy is constant
B.
is acceleration is constant
C.
its velocity is constant
D.
it moves in a straight line
2004
JEE Mains
MCQ
AIEEE 2004
A force $\overrightarrow F = \left( {5\overrightarrow i + 3\overrightarrow j + 2\overrightarrow k } \right)N$ is applied over a particle which displaces it from its origin to the point $\overrightarrow r = \left( {2\overrightarrow i - \overrightarrow j } \right)m.$ The work done on the particle in joules is
A.
$+10$
B.
$+7$
C.
$-7$
D.
$+13$
2004
JEE Mains
MCQ
AIEEE 2004
A body of mass $' m ',$ acceleration uniformly from rest to $'{v_1}'$ in time ${T}$. The instantaneous power delivered to the body as a function of time is given by
A.
${{m{v_1}{t^2}} \over {{T}}}$
B.
${{mv_1^2t} \over {T^2}}$
C.
${{m{v_1}t} \over {{T}}}$
D.
${{mv_1^2t} \over {{T}}}$
2004
JEE Mains
MCQ
AIEEE 2004
A uniform chain of length $2$ $m$ is kept on a table such that a length of $60$ $cm$ hangs freely from the edge of the table. The total mass of the chain is $4$ $kg.$ What is the work done in pulling the entire chain on the table?
A.
$12$ $J$
B.
$3.6$ $J$
C.
$7.2$ $J$
D.
$1200$ $J$
2003
JEE Mains
MCQ
AIEEE 2003
A spring of spring constant $5 \times {10^3}\,N/m$ is stretched initially by $5$ $cm$ from the unstretched position. Then the work required to stretch it further by another $5$ $cm$ is
A.
$12.50$ $N$-$m$
B.
$18.75$ $N$-$m$
C.
$25.00$ $N$-$m$
D.
$625$ $N$-$m$