# Solved papers for JEE Main & Advanced Physics Work, Energy, Power & Collision / कार्य, ऊर्जा और शक्ति JEE PYQ - Work Energy Power and Collision

### done JEE PYQ - Work Energy Power and Collision Total Questions - 81

• question_answer1) A spring of force constant 800 N/m has an extension of 5 cm. The work done in extending it from 5 cm to 15 cm is                   [AIEEE 2002]

A)
16 J

B)
8 J

C)
32 J

D)
24 J

• question_answer2)  Consider the following two statements A. Linear momentum of a system of particles is zero. B. Kinetic energy of a system of particles is zero. Then,                                       [AIEEE 2003]

A)
A does not imply B and B does not imply A

B)
A implies B but B does not imply A

C)
A does not imply B but B implies A

D)
A implies B and B implies A

• question_answer3) A wire suspended vertically from one of its ends is stretched by attaching a weight of 200 N to the lower end. The weight stretches the wire by 1 mm. Then, the elastic energy stored in the wire is [AIEEE 2003]

A)
$0.2$ J

B)
10 J

C)
20 J

D)
$0.1$J

• question_answer4) A spring of spring constant 5 ´ 103 N/m is stretched initially by 5 cm from the upstretched position. Then, the work required to stretch it further by another 5 cm is           [AIEEE 2003]

A)
$12.50$N-m

B)
$18.75$N-m

C)
$25.00$ N-m

D)
$6.25$ N-m

• question_answer5) A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time t is proportional to                           [AIEEE 2003]

A)
${{t}^{3/4}}$

B)
${{t}^{3/2}}$

C)
${{t}^{1/4}}$

D)
${{t}^{1/2}}$

• question_answer6) 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?                     [AIEEE 2004]

A)
7.2 J

B)
3.6 J

C)
120 J

D)
1200 J

• question_answer7) A body of mass m accelerates uniformly from rest to${{v}_{1}}$in time${{t}_{1}}$. The instantaneous power delivered to the body as a function of time t is [AIEEE 2004]

A)
$\frac{m{{v}_{1}}t}{{{t}_{1}}}$

B)
$\frac{mv_{1}^{2}t}{t_{1}^{2}}$

C)
$\frac{m{{v}_{1}}{{t}^{2}}}{{{t}_{1}}}$

D)
$\frac{mv_{1}^{2}t}{{{t}_{1}}}$

• question_answer8) 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 particle takes place in a plane, it follows that [AIEEE 2004]

A)
its velocity is constant

B)
its acceleration is constant

C)
its kinetic energy is constant

D)
it moves in a straight line

• question_answer9) 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                                         [AIEEE 2005]

A)
40 m/s

B)
20 m/s

C)
10 m/s

D)
10V30m/s

• question_answer10)  The block of mass M moving on the frictionless horizontal surface collides with the spring of spring constant k and compresses it by length L. The maximum momentum of the block after collision is           [AIEEE 2005]

A)
$\sqrt{MK}L$

B)
$\frac{k{{L}^{2}}}{2M}$

C)
zero

D)
$\frac{M{{L}^{2}}}{k}$

• question_answer11) A mass m moves with a velocity v and collides   inelastically   with   another identical mass. After collision the 1st mass moves with velocity$\frac{v}{\sqrt{3}}$in a direction perpendicular to the initial direction of motion. Find the speed of the second mass after collision.                             [AIEEE 2005]

A)
$v$

B)
$\sqrt{3}v$

C)
$\frac{2}{\sqrt{3}}v$

D)
$\frac{v}{\sqrt{3}}$

• question_answer12) 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                               [AIEEE 2005]

A)
$\frac{m{{v}^{2}}}{{{T}^{2}}}t$

B)
$\frac{m{{v}^{2}}}{{{T}^{2}}}{{t}^{2}}$

C)
$\frac{1}{2}\frac{m{{v}^{2}}}{{{T}^{2}}}{{t}^{2}}$

D)
$\frac{1}{2}\frac{m{{v}^{2}}}{{{T}^{2}}}{{t}^{2}}$

• question_answer13) 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     [AIEEE 2006]

A)
$Mg(\sqrt{2}+1)$

B)
$Mg\sqrt{2}$

C)
$\frac{Mg}{\sqrt{2}}$

D)
$Mg(\sqrt{2}-1)$

• question_answer14) A particle of mass 100 g 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                      [AIEEE 2006]

A)
$-0.5J$

B)
$-125J$

C)
1.25J

D)
0.5J

• question_answer15) 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$g=10\text{ }m/{{s}^{2}}$]             [AIEEE 2006]

A)
4N

B)
16N

C)
20N

D)
22N

• question_answer16)  The potential energy of a 1 kg particle free to move along the x-axis is given by $V(x)=\left( \frac{{{x}^{4}}}{4}-\frac{{{x}^{2}}}{2} \right)J$ The total mechanical energy of the particle is 2 J. Then, the maximum speed (in m/s) is [AIEEE 2006]

A)
$3/\sqrt{2}$

B)
$\sqrt{2}$

C)
$1/\sqrt{2}$

D)
2

• question_answer17) A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10000 N/m. The spring compresses by                                                            [AIEEE 2007]

A)
9.34cm

B)
2.5cm

C)
11.0cm

D)
8.5cm

• question_answer18) A block of mass 0.50 kg is moving with a speed of 2.00 $m{{s}^{-1}}$ on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is [AIEEE 2008]

A)
0.67 J

B)
0.34 J

C)
0.16 J

D)
1.00 J

• question_answer19) An athlete in the Olympic Games covers a distance of 100m in 10s. His kinetic energy can be estimated to be in the range   [AIEEE 2008]

A)
20,000 J - 50,000 J

B)
2,000 J - 5,000 J

C)
200 J - 500 J

D)
$2\times {{10}^{5}}J-3\times {{10}^{5}}J$

• question_answer20)  Statement- 1: Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.      [AIEEE 2010] Statement- 2: Principle of conservation of momentum holds true for all kinds of collisions.

A)
Statement-1 is true, Statement-2 is false.

B)
Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1

C)
Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.

D)
Statement-1 is false, Statement-2 is true.

• question_answer21) The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U(x)=\frac{a}{{{x}^{12}}}-\frac{b}{{{x}^{6}}}$where a and b are constants and$x$is the distance between the atoms. If the dissociation energy of the molecule is $D=[U(x=\infty )-{{U}_{at\,equilibrium}}],D$is - [AIEEE 2010]

A)
$\frac{{{b}^{2}}}{6a}$

B)
$\frac{{{b}^{2}}}{2a}$

C)
$\frac{{{b}^{2}}}{12a}$

D)
$\frac{{{b}^{2}}}{4a}$

• question_answer22) At time t = 0s a particle starts moving along the x-axis. If its kinetic energy increases uniformly with time 't', the net force acting on it must be proportional to :                   [AIEEE 11-05-2011]

A)
constant

B)
t

C)
$\frac{1}{\sqrt{t}}$

D)
$\sqrt{t}$

• question_answer23)  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 ${{S}_{1}}$, will be more than that on ${{S}_{2}}$ Statement 2:  ${{k}_{1}}<{{k}_{2}}$                      [AIEEE 2012]

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, and Statement 2 is the correct explanation for statement 1

D)
Statement 1 is true, Statement 2 is true, and Statement 2 is not the correct explanation of Statement 1

• question_answer24) An engine pumps water continuously through a hose. Water leaves the hose with velocity v and m is mass per unit length of the water jet. If this jet hits a surface and came to rest instantaneously, the force on the surface is  [JEE ONLINE 07-05-2012]

A)
$m{{v}^{3}}$

B)
$m{{v}^{2}}$

C)
$\frac{1}{2}m{{v}^{2}}$

D)
$\frac{1}{2}m{{v}^{3}}$

• question_answer25) A particle gets displaced by $\Delta \overline{r}=\left( 2\hat{i}+3\hat{j}+4\hat{k} \right)m$ under the action of a force $\vec{F}=\left( 7\hat{i}+4\hat{j}+3\hat{k} \right).$ The change in its kinetic energy is   [JEE ONLINE 07-05-2012]

A)
38 J

B)
70J

C)
52.5 J

D)
126 J

• question_answer26)  Two bodies A and B of mass m and 2m respectively are placed on a smooth floor. They are connected by a spring of negligible mass. A' third body C of mass m is placed on the floor. The body C moves with a velocity ${{v}_{0}}$ along the line joining A and B and collides elastically with A. At a certain time after the collision it is found that the instantaneous velocities of A and B are same and the compression of the spring is ${{x}_{0}}$.                    [JEE ONLINE 12-05-2012] The spring constant k will be

A)
$m\frac{v_{0}^{2}}{x_{0}^{2}}$

B)
$m\frac{{{v}_{0}}}{2{{x}_{0}}}$

C)
$2m\frac{{{v}_{0}}}{{{x}_{0}}}$

D)
$\frac{2}{3}m{{\left( \frac{{{v}_{0}}}{{{x}_{0}}} \right)}^{2}}$

• question_answer27)  A spring is compressed between two blocks of masses ${{m}_{1}}$ and ${{m}_{2}}$ placed on a horizontal frictionless surface as shown in the figure. When the blocks are released, they have initial velocity of ${{v}_{1}}$ and ${{v}_{2}}$ as shown. The blocks travel distances ${{x}_{1}}$ and ${{x}_{2}}$ respectively before coming  to rest. The ratio $\left( \frac{{{x}_{1}}}{{{x}_{2}}} \right)$ is [JEE ONLINE 12-05-2012]

A)
$\frac{{{m}_{2}}}{{{m}_{1}}}$

B)
$\frac{{{m}_{1}}}{{{m}_{2}}}$

C)
$\sqrt{\frac{{{m}_{2}}}{{{m}_{1}}}}$

D)
$\sqrt{\frac{{{m}_{1}}}{{{m}_{2}}}}$

• question_answer28) A moving particle of mass m, makes a head on elastic collision with another particle of mass 2m, which is initially at rest. The percentage loss in energy of the colliding particle on collision, is close to [JEE ONLINE 19-05-2012]

A)
33%

B)
67%

C)
90%

D)
10%

• question_answer29)  The force $\overset{\to }{\mathop{F}}\,=F\hat{i}$ on a particle of mass 2 kg, moving along the x-axis is given in the figure as a function of its position x. The particle is moving with a velocity of 5 m/s along the x-axis at x = 0. What is the kinetic energy of the particle at $x=8m?$ [JEE ONLINE 26-05-2012]

A)
34 J

B)
34.5 J

C)
4.5 J

D)
29.4 J

• question_answer30) A ball is dropped vertically downwards from a height h above the ground. It hits the ground in elastically and bounces up vertically. Neglecting subsequent motion and air resistance, which of the following graph represents variation between speed (v) and height correctly? [JEE ONLINE 26-05-2012]

A)

B)

C)

D)

• question_answer31)  This question has statement I and Statement II. Of the four choice given after the statements, choose the one that best describes the two statements. Statement - I: A Point particle of mass m moving with speed v collides with stationary point particle of mass M. If the maximum energy loss possible is given as $f\left( \frac{1}{2}m{{v}^{2}} \right)$then$f=\left( \frac{m}{M+m} \right)$ Statement - II: Maximum energy loss occurs when the particles get stuck together as a result of the collision.                       [JEE MAIN 2013]

A)
Statement - I is true, Statement - II is true, statement - II is a correct explanation of Statement  I

B)
Statement - I is true, Statement - II is true, statement - II is not a correct explanation of Statement  I

C)
Statement - I is true, Statement - II is false

D)
Statement - I is false, Statement - II is true

• question_answer32) A wind -powered generator converts wind energy into electrical energy. Assume that the generator coverts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed $\upsilon$, the electrical power output will be most likely proportional to:                            [JEE ONLINE 25-04-2013]

A)
${{\nu }^{4}}$

B)
${{\nu }^{2}}$

C)
$\nu$

D)
${{\nu }^{3}}$

• question_answer33) When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude $F=ax+b{{x}^{2}}$where a and b are constants. The work done in stretching the un stretched rubber-band by L is:         [JEE MAIN 2014]

A)
$\frac{a{{L}^{2}}}{2}+\frac{b{{L}^{3}}}{3}$

B)
$\frac{1}{2}\left[ \frac{a{{L}^{2}}}{2}+\frac{b{{L}^{3}}}{3} \right]$

C)
$a{{L}^{2}}+b{{L}^{3}}$

D)
$\frac{1}{2}(a{{L}^{2}}+b{{L}^{3}})$

• question_answer34) A body of mass 5 kg under the action of constant force $\overset{\to }{\mathop{F}}\,={{F}_{x}}\hat{i}+{{F}_{y}}\hat{j}$has velocity at$t=0s$as$\overset{\to }{\mathop{v}}\,=\left( 6\hat{i}-2\hat{j} \right)m/s$and at t = 10s as $\overset{\to }{\mathop{v}}\,=+6\hat{j}\,m/s.$ The force $\overset{\to }{\mathop{F}}\,$is: [JEE ONLINE 11-04-2014]

A)
$\left( -3\hat{j}+4\hat{j} \right)N$

B)
$\left( -\frac{3}{5}\hat{i}+\frac{4}{5}\hat{j} \right)N$

C)
$\left( 3\hat{i}-4\hat{j} \right)N$

D)
$\left( \frac{3}{5}\hat{i}-\frac{4}{5}\hat{j} \right)N$

• question_answer35) The average mass of rain drops is $3.0\times {{10}^{-5}}$kg and their avarage terminal velocity is 9 m/s. Calculate the energy transferred by rain to each square metre of the surface at a place which receives 100 cm of rain in a year.          [JEE ONLINE 11-04-2014]

A)
$3.0\times {{10}^{5}}J$

B)
$4.05\times {{10}^{4}}J$

C)
$3.0\times {{10}^{5}}J$

D)
$9.0\times {{10}^{4}}J$

• question_answer36)  Three masses m, 2m and 3m are moving in x-y plane with speed 3u, 2u and u respectively as shown in figure. The three masses collide at the same point at P and stick together. The velocity of resulting mass will be: [JEE ONLINE 12-04-2014]

A)
$\frac{u}{12}\left( \hat{i}+\sqrt{3}\hat{j} \right)$

B)
$\frac{u}{12}\left( \hat{i}-\sqrt{3}\hat{j} \right)$

C)
$\frac{u}{12}\left( -\hat{i}+\sqrt{3}\hat{j} \right)$

D)
$\frac{u}{12}\left( -\hat{i}-\sqrt{3}\hat{j} \right)$

• question_answer37) A spring of unstretched length l has a mass m with one end fixed to a rigid support. Assuming spring to be made of a uniform wire, the kinetic energy possessed by it if its free end is pulled with uniform velocity v is: [JEE ONLINE 12-04-2014]

A)
$\frac{1}{2}m{{v}^{2}}$

B)
$m{{v}^{2}}$

C)
$\frac{1}{3}m{{v}^{2}}$

D)
$\frac{1}{6}m{{v}^{2}}$

• question_answer38)  A particle is released on a vertical smooth semicircular track from point X so that OX makes angle q from the vertical (see figure). The normal reaction of the track on the particle vanishes at point Y where OY makes angle $\phi$ with the horizontal. Then: [JEE ONLINE 19-04-2014]

A)
$\sin \phi =\cos \phi$

B)
$\sin \phi =\frac{1}{2}\cos \theta$

C)
$\sin \phi =\frac{2}{3}\cos \theta$

D)
$\sin \phi =\frac{3}{4}\cos \theta$

• question_answer39) A particle of mass m moving in the x direction with speed 2v is hit by another particle of mass 2m moving in the y direction with speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to: [JEE MAIN 2015]

A)
56 %

B)
62 %

C)
44 %

D)
50 %

• question_answer40)  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 r, 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 $\frac{\upsilon }{10}$ after being dropped from height H, then neglecting energy losses and taking $g=10m{{s}^{-2}},$the value of H is close to: [JEE ONLINE 10-04-2015]

A)
0.2 km

B)
0.4 km

C)
0.5 km

D)
0.3 km

• question_answer41)  A block of mass m = 0.1 kg is connected to a spring of unknown spring constant k. It is compressed to a distance x from its equilibrium position and released from rest. After approaching half the distance $\left( \frac{x}{2} \right)$from equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with a velocity $3m{{s}^{-1}}.$ The total initial energy of the spring is: [JEE ONLINE 10-04-2015]

A)
15 J

B)
0.6 J

C)
0.8 J

D)
0.3 J

• question_answer42)  A particle is moving in a circle of radius r under the action of a force $F=\alpha {{r}^{2}}$which is directed towards centre of the circle. [JEE MAIN 11-04-2015] Total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy=0 for r=0):

A)
$\alpha {{r}^{3}}$

B)
$\frac{1}{2}\alpha {{r}^{3}}$

C)
$\frac{4}{3}\alpha {{r}^{3}}$

D)
$\frac{5}{6}\alpha {{r}^{3}}$

• question_answer43)  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 $\text{3}.\text{8}\times \text{1}0\text{7J}$of energy per kg which is converted to mechanical energy with a 20% efficiency rate. Take g = 9.8 ms-2:-[JEE MAIN - I 3-4-2016]

A)
$\text{12}.\text{89}\times \text{1}{{0}^{\text{3}}}\text{kg}$

B)
$\text{2}.\text{45}\times \text{1}{{0}^{\text{3}}}\text{kg}$

C)
$\text{6}.\text{45}\times \text{1}{{0}^{\text{3}}}\text{kg}$

D)
$\text{9}.\text{89}\times \text{1}{{0}^{\text{3}}}\text{kg}$

• question_answer44)  A point particle of mass, moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals m. The particle is released, from rest, from the point P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and PR, of the track, are equal to each other, and no energy is lost when particle changes direction from PQ to QR. [JEE MAIN - I 3-4-2016] The values of the coefficient of friction m and the distance x(=QR) are, respectively close to:-

A)
0.29 and 6.5 m

B)
0.2 and 6.5 m

C)
0.2 and 3.5 m

D)
0.29 and 3.5 m

• question_answer45) A car of weight W is on an inclined road that rises by 100 m over a distance of 1km and applies a constant frictional force $\frac{W}{20}$ on the car. While moving uphill on the road at a speed of $10m{{s}^{-1}},$the car needs power $\frac{P}{2}$If it needs power while moving downhill at speed v then value of v is:       [JEE ONLINE 09-04-2016]

A)
$5\,m{{s}^{-1}}$

B)
$20\,m{{s}^{-1}}$

C)
$10\,m{{s}^{-1}}$

D)
$15\,m{{s}^{-1}}$

• question_answer46) Concrete mixture is made by mixing cement, stone and sand in a rotating cylindrical drum. If the drum rotates too fast, the ingredients remain stuck to the wall of the drum and proper mixing of ingredients does not take place. The maximum rotational speed of the drum in revolutions per minute (rpm) to ensure proper mixing is close to:             (Take the radius of the drum to be 1.25m and its axle to be horizontal): [JEE ONLINE 10-04-2016]

A)
1.3

B)
0.4

C)
27.0

D)
None of these

• question_answer47)  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:                                               [JEE ONLINE 10-04-2016]

A)
12000 J

B)
12000 J

C)
4500 J

D)
9300 J

• question_answer48) A body of mass $m={{10}^{-2}}kg$is moving in a medium and experiences a frictional force $m={{10}^{-2}}kg$Its intial speed is ${{v}_{0}}=10m{{s}^{-1}}.$If, after 10 s, its energy is$\frac{1}{8}mv_{0}^{2},$ [JEE Main 2017]

A)
${{10}^{-4}}kg\,{{m}^{-1}}$

B)
${{10}^{-1}}kg\,{{m}^{-1}}{{S}^{-1}}$

C)
${{10}^{-3}}kg\,{{m}^{-1}}$

D)
${{10}^{-3}}kg\,{{s}^{-1}}$

• question_answer49) 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:                                    [JEE Main 2017]

A)
9 J

B)
18 J

C)
4.5 J

D)
22 J

• question_answer50) 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 [JEE Online 08-04-2017]

A)
2h

B)
$\infty$

C)
$\frac{5}{3}h$

D)
None of these

• question_answer51)  Two particles A and B of equal mass M are moving with the same speed $\upsilon$ as shown in the figure. They collide completely in elastically and move as a single particle C. The angle $\theta$ that the path of C makes with the X-axis is given by [JEE Online 09-04-2017]

A)
$\tan \theta \,=\frac{\sqrt{3}-\sqrt{2}}{1-\sqrt{2}}$

B)
$\tan \theta \,=\frac{1-\sqrt{2}}{\sqrt{2}(1+\sqrt{3})}$

C)
$\tan \theta \,\frac{1-\sqrt{3}}{1+\sqrt{2}}$

D)
$\tan \theta \,=\frac{\sqrt{3}+\sqrt{2}}{1-\sqrt{2}}$

• question_answer52) It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is ${{\text{P}}_{\text{d}}}$; while for its similar collision with carbon nucleus at rest, fractional loss of energy is${{\text{P}}_{\text{c}}}$. The values of ${{\text{P}}_{\text{d}}}$and ${{\text{P}}_{\text{c}}}$are respectively: [JEE Main Online 08-04-2018]

A)
$\text{(0, 0)}$

B)
$\text{(0, 1)}$

C)
$\text{(}\cdot 89\text{, }\cdot \text{28)}$

D)
$\text{(}\cdot 28\text{, }\cdot \text{89)}$

• question_answer53) A particle is moving in a circular path of radius a under the action of an attractive potential $\text{U=-}\frac{\text{k}}{\text{2}{{\text{r}}^{\text{2}}}}$. Its total energy is : [JEE Main Online 08-04-2018]

A)
Zero

B)
$\text{-}\frac{\text{k}}{\text{4 }{{\text{a}}^{\text{2}}}}$

C)
$\frac{k}{2{{a}^{2}}}$

D)

• question_answer54) In a collinear collision, a particle with an initial speed ${{v}_{o}}$ strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative velocity between the two particles/after collision, is: [JEE Main Online 08-04-2018]

A)
$\frac{{{v}_{o}}}{2}$

B)
$\frac{{{v}_{o}}}{\sqrt{2}}$

C)
$\frac{{{v}_{o}}}{4}$

D)
$\sqrt{2}{{v}_{o}}$

• question_answer55) The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants $G,h$ and$c$. Which of the following correctly gives the Planck length? [JEE Online 15-04-2018 (II)]

A)
${{G}^{2}}hc$

B)
${{\left( \frac{Gh}{{{c}^{3}}} \right)}^{\frac{1}{2}}}$

C)
${{G}^{\frac{1}{2}}}{{h}^{2}}c$

D)
$G{{h}^{2}}{{c}^{3}}$

• question_answer56) A proton of mass $m$ collides elastically with a particle of unknown mass at rest. After the collision, the proton and the unknown particle are seen moving at an angle of $90{}^\circ$ with respect to each other. The mass of unknown particle is: [JEE Online 15-04-2018 (II)]

A)
$\frac{m}{\sqrt{3}}$

B)
$\frac{m}{2}$

C)
$2m$

D)
$m$

• question_answer57) A body of mass starts moving from rest along x-axis so that its velocity varies as$v=a\sqrt{s}$ where is a constant and is the distance covered by the body. The total work done by all the forces acting on the body in the first seconds after the start of the motion is: [JEE Main Online 16-4-2018]

A)
$\frac{1}{8}m{{a}^{4}}{{t}^{2}}$

B)
$4m{{a}^{4}}{{t}^{2}}$

C)
$8m{{a}^{4}}{{t}^{2}}$

D)
$\frac{1}{4}m{{a}^{4}}{{t}^{2}}$

• question_answer58)  A block of mass m, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant k. The other end of the spring is fixed, as shown in the figure. The block is initally at rest in its equilibrium position. If now the block is pulled with a constant force F, the maximum speed of the block is-[JEE Main 09-Jan-2019 Morning]

A)
$\frac{2F}{\sqrt{mk}}$

B)
$\frac{\pi \,F}{\sqrt{mk}}$

C)
$\frac{F}{\pi \,\sqrt{mk}}$

D)
$\frac{F}{\sqrt{mk}}$

• question_answer59)  Three blocks A, B and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal masses, m while C has mass M. Block A is given an initial speed v towards B due to which it collides with B perfectly inelastically $\frac{5}{6}th$ of the initial kinetic energy is lost in whole process. What is value of M/m? [JEE Main 09-Jan-2019 Morning]

A)
2

B)
3

C)
5

D)
4

• question_answer60) A force acts on a 2 kg object so that its position is given as a function of time as$x=3{{t}^{2}}+5$. What is the work done by this force in first 5 seconds?   [JEE Main 09-Jan-2019 Evening]

A)
950 J

B)
900 J

C)
875 J

D)
850 J

• question_answer61)  A block of mass m is kept on a platform which starts from rest with constant acceleration $g/2$ acceleration $g/2$ upward, as shown in figure. Work done by normal reaction on block in time is-[JEE Main 10-Jan-2019 Morning]

A)
$\frac{m{{g}^{2}}{{t}^{2}}}{8}$

B)
$\frac{3\,m{{g}^{2}}{{t}^{2}}}{8}$

C)
$-\frac{\,m{{g}^{2}}{{t}^{2}}}{8}$

D)
0

• question_answer62) A particle which is experiencing a force, given by $\overrightarrow{F}=3\overrightarrow{i}-12\overrightarrow{j}$, undergoes a displacement of $\overrightarrow{d}=4\overrightarrow{i}$ . If 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? [JEE Main 10-Jan-2019 Evening]

A)
9 J

B)
10 J

C)
12 J

D)
15 J

• question_answer63) A body of mass 1 kg falls freely from a height of 100 m, on a platform of mass 3 kg which is mounted on a spring having spring constant $k=1.25\times {{10}^{6}}N/m.$The body sticks to the platform and the spring's maximum compression is found to be x. Given that $g=10\,m{{s}^{-2}},\,$the value of x will be close to- [JEE Main 11-Jan-2019 Morning]

A)
8 cm

B)
40 cm

C)
80 cm

D)
None of these

• question_answer64) In a Youngs double slit experiment, the path difference, at a certain point on the screen, between two interfering waves is $\frac{1}{8}th$ of wavelength. The ratio of the intensity at this point to that at the centre of a bright fringe is close to-   [JEE Main 11-Jan-2019 Morning]

A)
0.80

B)
0.94

C)
0.85

D)
0.74

• question_answer65) 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 so that its momentum changes from? to 3p. Here k is a constant. The value of T is- [JEE Main 11-Jan-2019 Evening]

A)
$2\sqrt{\frac{p}{k}}$

B)
$\sqrt{\frac{2k}{p}}$

C)
$\sqrt{\frac{2p}{k}}$

D)
$2\sqrt{\frac{k}{p}}$

• question_answer66)  Two light identical springs of spring constant k are attached horizontally at the two ends of a uniform horizontal rod AB of length l and mass m. The rod is pivoted at its centre O and can rotate freely in horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released.                          [JEE Main 12-Jan-2019 Morning] The frequency of resulting oscillation is

A)
$\frac{1}{2\pi }\sqrt{\frac{k}{m}}$

B)
$\frac{1}{2\pi }\sqrt{\frac{6k}{m}}$

C)
$\frac{1}{2\pi }\sqrt{\frac{3k}{m}}$

D)
$\frac{1}{2\pi }\sqrt{\frac{2k}{m}}$

• question_answer67) An alpha-particle of mass m suffers -dimensional elastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, 64% of its initial kinetic energy. The mass of the nucleus is- [JEE Main 12-Jan-2019 Evening]

A)
4 m

B)
1.5 m

C)
3.5 m

D)
2 m

• question_answer68) A rocket has to be launched from earth in such a way that it never returns. If E is the minimum energy delivered by the rocket launcher, what should be the minimum energy that the launcher should have if the same rocket is to be launched from the surface of the moon? Assume that the density of the earth and the moon are equal and that the earth's volume is 64 times the volume of the moon :-  [JEE Main 8-4-2019 Afternoon]

A)
$\frac{E}{4}$

B)
$\frac{E}{16}$

C)
$\frac{E}{32}$

D)
$\frac{E}{64}$

• question_answer69) A body of mass ${{m}_{1}}$ moving with an unknown velocity of ${{\text{v}}_{1}}\hat{i},$undergoes a collinear collision with a body of mass${{m}_{2}}$moving with a velocity ${{\text{v}}_{2}}\hat{i}.$After collision, ${{m}_{1}}$and ${{m}_{2}}$move with velocities of ${{\text{v}}_{3}}\hat{i}$and ${{\text{v}}_{4}}\hat{i},$respectively. If ${{m}_{2}}=0.5{{m}_{1}}$and ${{\text{v}}_{3}}=0.5{{\text{v}}_{1}},$then ${{\text{v}}_{1}}$is :- [JEE Main 8-4-2019 Afternoon]

A)
${{\text{v}}_{4}}-\frac{{{\text{v}}_{2}}}{4}$

B)
${{\text{v}}_{4}}-\frac{{{\text{v}}_{2}}}{2}$

C)
${{\text{v}}_{4}}-{{\text{v}}_{2}}$

D)
${{\text{v}}_{4}}\text{+}{{\text{v}}_{2}}$

• question_answer70) A body of mass 2 kg makes an eleastic collision with a second body at rest and continues to move in the original direction but with one fourth of its original speed. What is the mass of the second body? [JEE Main 9-4-2019 Morning]

A)
1.8 kg

B)
1.2 kg

C)
1.5 kg

D)
1.0 kg

• question_answer71) A ball is thrown vertically up (taken as +z-axis) from the ground. The correct momentum-height (p-h) diagram is : [JEE Main 9-4-2019 Morning]

A)

B)

C)

D)

• question_answer72) A uniform cable of mass 'M' and length 'L' is placed on a horizontal surface such that its ${{\left( \frac{1}{n} \right)}^{th}}$part is hanging below the edge of the surface. To lift the hanging part of the cable up to the surface, the work done should be :             [JEE Main 9-4-2019 Morning]

A)
$\frac{MgL}{{{n}^{2}}}$

B)
$\frac{MgL}{2{{n}^{2}}}$

C)
$\frac{2MgL}{{{n}^{2}}}$

D)
$nMgL$

• question_answer73) A wedge of mass M = 4m lies on a frictionless plane. A particle of mass m approaches the wedge with speed v. There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by :- [JEE Main 9-4-2019 Afternoon]

A)
$\frac{2{{\text{v}}^{2}}}{7g}$

B)
$\frac{{{\text{v}}^{2}}}{g}$

C)
$\frac{\text{2}{{\text{v}}^{2}}}{5g}$

D)
$\frac{{{\text{v}}^{2}}}{2g}$

• question_answer74)  Two particles, of masses M and 2M, moving, as shown, with speeds of 10 m/s and 5 m/s, collide elastically at the origin. After the collision, they move along the indicated directions with speeds${{\upsilon }_{1}}$and ${{\upsilon }_{2}}$, respectively. The values of ${{\upsilon }_{1}}$and ${{\upsilon }_{2}}$ are nearly:    [JEE Main 10-4-2019 Morning]

A)
3.2 m/s and 6.3 m/s

B)
3.2 m/s and 12.6 m/s

C)
6.5 m/s and 6.3 m/s

D)
6.5 m/s and 3.2 m/s

• question_answer75) A bullet of mass 20 g has an initial speed of $1m{{s}^{-1}},$ just before it starts penetrating a mud wall of thickness 20 cm. if the wall offers a mean resistance of $2.5\times {{10}^{2}}N,$the speed of the bullet after emerging from the other side of the wall is close to:     [JEE Main 10-4-2019 Afternoon]

A)
$0.4m{{s}^{-1}}$

B)
$0.1m{{s}^{-1}}$

C)
$0.3m{{s}^{-1}}$

D)
$0.7m{{s}^{-1}}$

• question_answer76)  A submarine travelling at 18 km/hr is being chased along the line of its velocity by another submarine travelling at 27 km/hr. B sends a sonar signal of 500 Hz to detect A and receives a reflected sound of frequency n. The value of n is close to: [JEE Main Held on 12-4-2019 Morning] (Speed of sound in water $=1500\text{ }m{{s}^{1}}$)

A)
499 Hz

B)
502 Hz

C)
507 Hz

D)
504 Hz

• question_answer77) 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: $(1\text{ }HP=746\text{ }W,\text{ }g=10\text{ }m{{s}^{2}})$ [JEE MAIN Held on 07-01-2020 Morning]

A)
$1.5\text{ }m{{s}^{1}}$

B)
$1.9\text{ }m{{s}^{1}}$

C)
$1.7\text{ }m{{s}^{1}}$

D)
$2.0\text{ }m{{s}^{1}}$

• question_answer78)  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 m), the kinetic energy of the particle (in J) is: (figure drawn is schematic and not to scale; take $g=10\text{ }m{{s}^{2}}$) [JEE MAIN Held on 07-01-2020 Morning]

• question_answer79)  Consider a force$\vec{F}=-x\hat{i}+y\hat{j}$. The work done by this force in moving a particle from point A(1, 0) to B(0, 1) along the line segment is : [JEE MAIN Held on 09-01-2020 Morning] (all quantities are in SI units)

A)
2

B)
1

C)
$\frac{1}{2}$

D)
$\frac{3}{2}$

• question_answer80) Two particles of equal mass m have respective initial velocities $u\hat{i}$and u $\left( \frac{\hat{i}+\hat{j}}{2} \right)$.They collide completely inelastically. The energy lost in the process is: [JEE MAIN Held on 09-01-2020 Morning]

A)
$\sqrt{\frac{2}{3}}m{{u}^{2}}$

B)
$\frac{3}{4}m{{u}^{2}}$

C)
$\frac{1}{8}m{{u}^{2}}$

D)
$\frac{1}{3}m{{u}^{2}}$

• question_answer81) A particle of mass m is projected with a speed u from the ground at an angle $\theta =\frac{\pi }{3}$w.r.t. horizontal (x-axis). When it has reached its maximum height, it collides completely inelastically with another particle of the same mass and velocity $u\hat{i}$. The horizontal distance covered by the combined mass before reaching the ground is [JEE MAIN Held on 09-01-2020 Evening]

A)
$\frac{5}{8}\frac{{{u}^{2}}}{g}$

B)
$\frac{3\sqrt{2}}{4}\frac{{{u}^{2}}}{g}$

C)
$\frac{3\sqrt{3}}{8}\,\,\frac{{{u}^{2}}}{g}$

D)
$2\sqrt{2}\frac{{{u}^{2}}}{g}$