Work Energy Power Solved Examples | Physics for JEE Main & Advanced PDF Download

 Page 1


Solved Examples on Work Power and 
Energy 
JEE Mains 
Q1.  A force  ?? ? ? 
= -?? (?? ??ˆ + ?? ??ˆ), where ?? is a positive constant, acts on a particle moving in the xy 
plane. 
Starting from the origin, the particle is taken along the positive ?? -axis to the point (?? ,?? ), and the 
parallel to the ?? -axis to the point (?? ,?? ). The total work done by the force on the particle is: 
(A) ?????? 
?? 
(B) ?? ????
?? 
(C) -????
?? 
(D) ????
?? 
Correct Answer: Option C 
Ans : (C) Work done = ????? .???? + ????? .????                                      
?? = ???? ??ˆ + ???? ??ˆ
???? = -???? ;???? = -????
?? = ?? 1-2
+ ?? 2-3
 ? ?
?? 0
????????? + ? ?
?? 0
????????? -? ?
?? 0
??? × 0 × ???? + ? ?
?? 0
?- ???????? = 0 + -???? (?? - 0) = -?? ?? 2
 
 
 
Q. 2 Supposing that the earth of mass ?? moves around the sun in a circular orbit of radius ' ?? ', 
the work done in half revolution is: 
(A) 
?? ?? ?? ?? ?????? 
(B) 
?? ?? ?? ?? × ?? ?? 
(C) Zero 
(D) None of these 
Ans : (C) Work done is zero as force and displacement are perpendicular to each other so F
? 
.ds
???? 
= 0 
Page 2


Solved Examples on Work Power and 
Energy 
JEE Mains 
Q1.  A force  ?? ? ? 
= -?? (?? ??ˆ + ?? ??ˆ), where ?? is a positive constant, acts on a particle moving in the xy 
plane. 
Starting from the origin, the particle is taken along the positive ?? -axis to the point (?? ,?? ), and the 
parallel to the ?? -axis to the point (?? ,?? ). The total work done by the force on the particle is: 
(A) ?????? 
?? 
(B) ?? ????
?? 
(C) -????
?? 
(D) ????
?? 
Correct Answer: Option C 
Ans : (C) Work done = ????? .???? + ????? .????                                      
?? = ???? ??ˆ + ???? ??ˆ
???? = -???? ;???? = -????
?? = ?? 1-2
+ ?? 2-3
 ? ?
?? 0
????????? + ? ?
?? 0
????????? -? ?
?? 0
??? × 0 × ???? + ? ?
?? 0
?- ???????? = 0 + -???? (?? - 0) = -?? ?? 2
 
 
 
Q. 2 Supposing that the earth of mass ?? moves around the sun in a circular orbit of radius ' ?? ', 
the work done in half revolution is: 
(A) 
?? ?? ?? ?? ?????? 
(B) 
?? ?? ?? ?? × ?? ?? 
(C) Zero 
(D) None of these 
Ans : (C) Work done is zero as force and displacement are perpendicular to each other so F
? 
.ds
???? 
= 0 
 
 
 
 
Q. 3 A string of mass ' ?? ' and length ' ?? ' rests over a frictionless table with ?? /?? th of its length 
hanging from a side. The work done in bringing the hanging part back on the table is: 
(A) ?????? /?? 
(B) ?????? /???? 
(C) ?????? /???? 
(D) None of these 
Ans : (B) By work energy theorem 
w
net 
= ?KE [assuming negligible K.E.] 
w
gravity 
+ w
force 
= 0
w
force 
= -(-
m
4
 g(
l
8
)) =
mgl
32
 
 
Q. 4 A weight ???? is suspended from a spring. If the elongation in the spring is ?? ?? ' the elastic 
energy stored in it is: 
(A) 
?? ?? ?????? ? 
 
(B) ?? ?????? ?? 
(C) ?????? ?? 
(D) 
?? ?? ?????? ?? 
Ans : (A) by force equilibrium 
kx
0
=
mg
x
0
 Elastic energy =
1
2
kx
0
2
=
1
2
mg
x
0
x
0
2
=
mgx
0
2
 
 
 
 
 
Page 3


Solved Examples on Work Power and 
Energy 
JEE Mains 
Q1.  A force  ?? ? ? 
= -?? (?? ??ˆ + ?? ??ˆ), where ?? is a positive constant, acts on a particle moving in the xy 
plane. 
Starting from the origin, the particle is taken along the positive ?? -axis to the point (?? ,?? ), and the 
parallel to the ?? -axis to the point (?? ,?? ). The total work done by the force on the particle is: 
(A) ?????? 
?? 
(B) ?? ????
?? 
(C) -????
?? 
(D) ????
?? 
Correct Answer: Option C 
Ans : (C) Work done = ????? .???? + ????? .????                                      
?? = ???? ??ˆ + ???? ??ˆ
???? = -???? ;???? = -????
?? = ?? 1-2
+ ?? 2-3
 ? ?
?? 0
????????? + ? ?
?? 0
????????? -? ?
?? 0
??? × 0 × ???? + ? ?
?? 0
?- ???????? = 0 + -???? (?? - 0) = -?? ?? 2
 
 
 
Q. 2 Supposing that the earth of mass ?? moves around the sun in a circular orbit of radius ' ?? ', 
the work done in half revolution is: 
(A) 
?? ?? ?? ?? ?????? 
(B) 
?? ?? ?? ?? × ?? ?? 
(C) Zero 
(D) None of these 
Ans : (C) Work done is zero as force and displacement are perpendicular to each other so F
? 
.ds
???? 
= 0 
 
 
 
 
Q. 3 A string of mass ' ?? ' and length ' ?? ' rests over a frictionless table with ?? /?? th of its length 
hanging from a side. The work done in bringing the hanging part back on the table is: 
(A) ?????? /?? 
(B) ?????? /???? 
(C) ?????? /???? 
(D) None of these 
Ans : (B) By work energy theorem 
w
net 
= ?KE [assuming negligible K.E.] 
w
gravity 
+ w
force 
= 0
w
force 
= -(-
m
4
 g(
l
8
)) =
mgl
32
 
 
Q. 4 A weight ???? is suspended from a spring. If the elongation in the spring is ?? ?? ' the elastic 
energy stored in it is: 
(A) 
?? ?? ?????? ? 
 
(B) ?? ?????? ?? 
(C) ?????? ?? 
(D) 
?? ?? ?????? ?? 
Ans : (A) by force equilibrium 
kx
0
=
mg
x
0
 Elastic energy =
1
2
kx
0
2
=
1
2
mg
x
0
x
0
2
=
mgx
0
2
 
 
 
 
 
 
 
Q. 5 A ball is thrown up with a certain velocity at angle ?? to the horizontal. The kinetic energy KE 
of the horizontal. The kinetic energy KE of the ball varies with horizontal displacement ?? as: 
 
 
 
 
 
Vertical velocity at height h is ?? ?? 
?? ?? = ?? sin ?? - ????
?? =
?? ?? cos ?? ?? ?? = ?? sin ?? -
????
?? cos ?? ???? =
1
2
?? [?? ?? 2
+ ?? ?? 2
] =
1
2
?? [?? 2
+
?? 2
?? 2
?? 2
cos
2
 ?? - 2tan ?????? ]
 
so graph (c) is correct 
 
 
Page 4


Solved Examples on Work Power and 
Energy 
JEE Mains 
Q1.  A force  ?? ? ? 
= -?? (?? ??ˆ + ?? ??ˆ), where ?? is a positive constant, acts on a particle moving in the xy 
plane. 
Starting from the origin, the particle is taken along the positive ?? -axis to the point (?? ,?? ), and the 
parallel to the ?? -axis to the point (?? ,?? ). The total work done by the force on the particle is: 
(A) ?????? 
?? 
(B) ?? ????
?? 
(C) -????
?? 
(D) ????
?? 
Correct Answer: Option C 
Ans : (C) Work done = ????? .???? + ????? .????                                      
?? = ???? ??ˆ + ???? ??ˆ
???? = -???? ;???? = -????
?? = ?? 1-2
+ ?? 2-3
 ? ?
?? 0
????????? + ? ?
?? 0
????????? -? ?
?? 0
??? × 0 × ???? + ? ?
?? 0
?- ???????? = 0 + -???? (?? - 0) = -?? ?? 2
 
 
 
Q. 2 Supposing that the earth of mass ?? moves around the sun in a circular orbit of radius ' ?? ', 
the work done in half revolution is: 
(A) 
?? ?? ?? ?? ?????? 
(B) 
?? ?? ?? ?? × ?? ?? 
(C) Zero 
(D) None of these 
Ans : (C) Work done is zero as force and displacement are perpendicular to each other so F
? 
.ds
???? 
= 0 
 
 
 
 
Q. 3 A string of mass ' ?? ' and length ' ?? ' rests over a frictionless table with ?? /?? th of its length 
hanging from a side. The work done in bringing the hanging part back on the table is: 
(A) ?????? /?? 
(B) ?????? /???? 
(C) ?????? /???? 
(D) None of these 
Ans : (B) By work energy theorem 
w
net 
= ?KE [assuming negligible K.E.] 
w
gravity 
+ w
force 
= 0
w
force 
= -(-
m
4
 g(
l
8
)) =
mgl
32
 
 
Q. 4 A weight ???? is suspended from a spring. If the elongation in the spring is ?? ?? ' the elastic 
energy stored in it is: 
(A) 
?? ?? ?????? ? 
 
(B) ?? ?????? ?? 
(C) ?????? ?? 
(D) 
?? ?? ?????? ?? 
Ans : (A) by force equilibrium 
kx
0
=
mg
x
0
 Elastic energy =
1
2
kx
0
2
=
1
2
mg
x
0
x
0
2
=
mgx
0
2
 
 
 
 
 
 
 
Q. 5 A ball is thrown up with a certain velocity at angle ?? to the horizontal. The kinetic energy KE 
of the horizontal. The kinetic energy KE of the ball varies with horizontal displacement ?? as: 
 
 
 
 
 
Vertical velocity at height h is ?? ?? 
?? ?? = ?? sin ?? - ????
?? =
?? ?? cos ?? ?? ?? = ?? sin ?? -
????
?? cos ?? ???? =
1
2
?? [?? ?? 2
+ ?? ?? 2
] =
1
2
?? [?? 2
+
?? 2
?? 2
?? 2
cos
2
 ?? - 2tan ?????? ]
 
so graph (c) is correct 
 
 
 
 
Q. 6 A body ?? ?? is projected upwards with velocity ?? ?? another body ?? ?? of same mass is projected 
at an angle of ????
°
. Both reach the same height. What is the ratio of their kinectic energies at the 
point of projection: 
(A) 1 
(B) ?? /?? 
(C) ?? /?? 
(D) ?? /?? 
Ans : (B) 
 
 Maximum height H =
u
2
sin
2
 ?? 2 g
H
1
=
v
1
2
2 g
;H
2
=
v
2
2
(
1
v2
)
2
2 g
=
v
2
2
ug
H
1
= H
2
 ?
v
1
2
2
=
v
2
2
4
v
2
2
= 2v
1
2
KE
1
KE
2
=
1/2 m
1
v
1
2
1/2 m
2
v
2
2
=
v
1
2
v
2
2
=
1
2
 
 
Q. 7 A uniform chain of length ?? and mass ?? is lying on a smooth table and one third of its length 
is hanging vertically down over the edge of the table. If ?? is acceleration due to gravity, then the 
work required to pull the hanging part onto the table is: 
(A) ?????? 
(B) 
?????? ?? 
(C) 
???????? ?? 
(D) 
?????? ????
 
Ans : (C) By work energy theorem 
W
net 
= ?KE[ Assuming negligible K.E. ]
w
gravity 
+ W
force 
= 0
 W
net 
= (-
1
18
mgl) - (-
1
2
mgl) =
4
9
mgl
 
Page 5


Solved Examples on Work Power and 
Energy 
JEE Mains 
Q1.  A force  ?? ? ? 
= -?? (?? ??ˆ + ?? ??ˆ), where ?? is a positive constant, acts on a particle moving in the xy 
plane. 
Starting from the origin, the particle is taken along the positive ?? -axis to the point (?? ,?? ), and the 
parallel to the ?? -axis to the point (?? ,?? ). The total work done by the force on the particle is: 
(A) ?????? 
?? 
(B) ?? ????
?? 
(C) -????
?? 
(D) ????
?? 
Correct Answer: Option C 
Ans : (C) Work done = ????? .???? + ????? .????                                      
?? = ???? ??ˆ + ???? ??ˆ
???? = -???? ;???? = -????
?? = ?? 1-2
+ ?? 2-3
 ? ?
?? 0
????????? + ? ?
?? 0
????????? -? ?
?? 0
??? × 0 × ???? + ? ?
?? 0
?- ???????? = 0 + -???? (?? - 0) = -?? ?? 2
 
 
 
Q. 2 Supposing that the earth of mass ?? moves around the sun in a circular orbit of radius ' ?? ', 
the work done in half revolution is: 
(A) 
?? ?? ?? ?? ?????? 
(B) 
?? ?? ?? ?? × ?? ?? 
(C) Zero 
(D) None of these 
Ans : (C) Work done is zero as force and displacement are perpendicular to each other so F
? 
.ds
???? 
= 0 
 
 
 
 
Q. 3 A string of mass ' ?? ' and length ' ?? ' rests over a frictionless table with ?? /?? th of its length 
hanging from a side. The work done in bringing the hanging part back on the table is: 
(A) ?????? /?? 
(B) ?????? /???? 
(C) ?????? /???? 
(D) None of these 
Ans : (B) By work energy theorem 
w
net 
= ?KE [assuming negligible K.E.] 
w
gravity 
+ w
force 
= 0
w
force 
= -(-
m
4
 g(
l
8
)) =
mgl
32
 
 
Q. 4 A weight ???? is suspended from a spring. If the elongation in the spring is ?? ?? ' the elastic 
energy stored in it is: 
(A) 
?? ?? ?????? ? 
 
(B) ?? ?????? ?? 
(C) ?????? ?? 
(D) 
?? ?? ?????? ?? 
Ans : (A) by force equilibrium 
kx
0
=
mg
x
0
 Elastic energy =
1
2
kx
0
2
=
1
2
mg
x
0
x
0
2
=
mgx
0
2
 
 
 
 
 
 
 
Q. 5 A ball is thrown up with a certain velocity at angle ?? to the horizontal. The kinetic energy KE 
of the horizontal. The kinetic energy KE of the ball varies with horizontal displacement ?? as: 
 
 
 
 
 
Vertical velocity at height h is ?? ?? 
?? ?? = ?? sin ?? - ????
?? =
?? ?? cos ?? ?? ?? = ?? sin ?? -
????
?? cos ?? ???? =
1
2
?? [?? ?? 2
+ ?? ?? 2
] =
1
2
?? [?? 2
+
?? 2
?? 2
?? 2
cos
2
 ?? - 2tan ?????? ]
 
so graph (c) is correct 
 
 
 
 
Q. 6 A body ?? ?? is projected upwards with velocity ?? ?? another body ?? ?? of same mass is projected 
at an angle of ????
°
. Both reach the same height. What is the ratio of their kinectic energies at the 
point of projection: 
(A) 1 
(B) ?? /?? 
(C) ?? /?? 
(D) ?? /?? 
Ans : (B) 
 
 Maximum height H =
u
2
sin
2
 ?? 2 g
H
1
=
v
1
2
2 g
;H
2
=
v
2
2
(
1
v2
)
2
2 g
=
v
2
2
ug
H
1
= H
2
 ?
v
1
2
2
=
v
2
2
4
v
2
2
= 2v
1
2
KE
1
KE
2
=
1/2 m
1
v
1
2
1/2 m
2
v
2
2
=
v
1
2
v
2
2
=
1
2
 
 
Q. 7 A uniform chain of length ?? and mass ?? is lying on a smooth table and one third of its length 
is hanging vertically down over the edge of the table. If ?? is acceleration due to gravity, then the 
work required to pull the hanging part onto the table is: 
(A) ?????? 
(B) 
?????? ?? 
(C) 
???????? ?? 
(D) 
?????? ????
 
Ans : (C) By work energy theorem 
W
net 
= ?KE[ Assuming negligible K.E. ]
w
gravity 
+ W
force 
= 0
 W
net 
= (-
1
18
mgl) - (-
1
2
mgl) =
4
9
mgl
 
 
 
 
Q. 8 A body is moved along a straight line by a machine delivering constant power. The distance 
moved by the body in time ?? is proportional to: 
(A) ?? ?? /?? 
(B) ?? ?? /?? 
(C) ?? ?? /?? 
(D) ?? ?? 
Ans : (C) ?? = ?? .?? 
?? = ???? .?? ?? = [
?????? ????
?? ]
 ? ?
?? 0
?
?????? ?? = ? ?
?? 0
??????? ?
?? ?? =
?? 2
2
?? =
v
2????
?? ? ?? ? ?? 1
2
+1
?? ? ?? 3/2
 
 
Q. 9 An alpha particle of energy ???????? is scattered through ??????
°
 by a fixed uranium nucleus. The 
distance of the closest approach is of the order of 
(A) ?? ?? 
(B) ????
-????
 ???? 
(C) ????
-????
 ???? 
(D) ????
-????
 ???? 
Ans : (C) Mechanical energy conservation 
KE
alpa 
+ ?? ?? ?? + ???? = ?? ?? electrostatic 
4 × 10
6
× 10
-19
=
9 × 10
10
× 10
-19
× 100× 10
-9
?? ?? ~ 10
-14
 m
?? ~ 10
-12
 cm
 
 
Q. 10 A simple pendulum has a string of length and bob of mass ?? . When the bob is at its lowest 
position, it is given the minimum horizontal speed necessary for it to move in a circular path about 
the point of suspension. The tension in the string at the lowest position of the bob is: 
(A) ?????? 
(B) ??????