Newton's Laws of Motion Solved Examples | Physics for JEE Main & Advanced PDF Download

 Page 1


Solved Examples on Newton’s Laws 
of Motion 
 
JEE Mains 
Q1: Two forces are such that the sum of their magnitudes is ???? ?? and their 
resultant is perpendicular to the smaller force and magnitude of resultant is 12 . 
Then the magnitudes of the forces are 
(a)???? ?? ,?? ?? 
(b) ???? ?? ,?? ?? 
(c) ???? ?? ,?? ?? 
(d) 11N, 7N 
Ans: (b)  
 
Let two forces are ?? 1
 and ?? 2
(?? 1
< ?? 2
) . 
According to problem: ?? 1
+ ?? 2
= 18 
Angle between ?? 1
 and resultant (?? ) is 90
°
 
 ? tan 90 =
?? 2
sin ?? ?? 1
+ ?? 2
cos ?? = 8
 ? ?? 1
+ ?? 2
cos ?? = 0
 ? cos ?? = -
?? 1
?? 2
 and ?? 2
= ?? 1
2
+ ?? 2
2
+ 2?? 1
?? 2
cos ?? 144= ?? 1
2
+ ?? 2
2
+ 2?? 1
?? 2
cos ?? 
by solving (i), (ii) and (iii) we get ?? 1
= 5 N and ?? 2
= 13 N 
 
Q2: In the following figure the masses of the blocks ?? and ?? are same and each 
equal to ?? . The tensions in the strings ???? and ???? are ?? ?? and ?? ?? respectively. The 
system is in equilibrium with a constant horizontal force ???? on ?? . The ?? ?? is 
(a) ???? 
(b) v?? ???? 
Page 2


Solved Examples on Newton’s Laws 
of Motion 
 
JEE Mains 
Q1: Two forces are such that the sum of their magnitudes is ???? ?? and their 
resultant is perpendicular to the smaller force and magnitude of resultant is 12 . 
Then the magnitudes of the forces are 
(a)???? ?? ,?? ?? 
(b) ???? ?? ,?? ?? 
(c) ???? ?? ,?? ?? 
(d) 11N, 7N 
Ans: (b)  
 
Let two forces are ?? 1
 and ?? 2
(?? 1
< ?? 2
) . 
According to problem: ?? 1
+ ?? 2
= 18 
Angle between ?? 1
 and resultant (?? ) is 90
°
 
 ? tan 90 =
?? 2
sin ?? ?? 1
+ ?? 2
cos ?? = 8
 ? ?? 1
+ ?? 2
cos ?? = 0
 ? cos ?? = -
?? 1
?? 2
 and ?? 2
= ?? 1
2
+ ?? 2
2
+ 2?? 1
?? 2
cos ?? 144= ?? 1
2
+ ?? 2
2
+ 2?? 1
?? 2
cos ?? 
by solving (i), (ii) and (iii) we get ?? 1
= 5 N and ?? 2
= 13 N 
 
Q2: In the following figure the masses of the blocks ?? and ?? are same and each 
equal to ?? . The tensions in the strings ???? and ???? are ?? ?? and ?? ?? respectively. The 
system is in equilibrium with a constant horizontal force ???? on ?? . The ?? ?? is 
(a) ???? 
(b) v?? ???? 
(c) v?? ???? 
(d) v?? ???? 
 
Ans: (b) From the free body diagram of block ?? 
 
?? 1
cos ?? 1
= ???? .
?? 1
sin ?? 1
= -???? .
 
by squaring and adding ?? 1
2
(sin
2
 ?? 1
+ cos
2
 ?? 1
)= 2(???? )
2
 
? ?? 1
= v2???? 
Q3: A block of mass ???? ???? is suspended through two light spring balances as 
shown in given Figure. 
(A) Both the scales will read ???? ???? 
(B) Both the scales will read ?? ???? . 
(C) The upper scales will read ???? ???? and the lower zero. 
(D) The readings may be anything but their sum will be ???? ???? 
Ans: (A) At point A; 
Page 3


Solved Examples on Newton’s Laws 
of Motion 
 
JEE Mains 
Q1: Two forces are such that the sum of their magnitudes is ???? ?? and their 
resultant is perpendicular to the smaller force and magnitude of resultant is 12 . 
Then the magnitudes of the forces are 
(a)???? ?? ,?? ?? 
(b) ???? ?? ,?? ?? 
(c) ???? ?? ,?? ?? 
(d) 11N, 7N 
Ans: (b)  
 
Let two forces are ?? 1
 and ?? 2
(?? 1
< ?? 2
) . 
According to problem: ?? 1
+ ?? 2
= 18 
Angle between ?? 1
 and resultant (?? ) is 90
°
 
 ? tan 90 =
?? 2
sin ?? ?? 1
+ ?? 2
cos ?? = 8
 ? ?? 1
+ ?? 2
cos ?? = 0
 ? cos ?? = -
?? 1
?? 2
 and ?? 2
= ?? 1
2
+ ?? 2
2
+ 2?? 1
?? 2
cos ?? 144= ?? 1
2
+ ?? 2
2
+ 2?? 1
?? 2
cos ?? 
by solving (i), (ii) and (iii) we get ?? 1
= 5 N and ?? 2
= 13 N 
 
Q2: In the following figure the masses of the blocks ?? and ?? are same and each 
equal to ?? . The tensions in the strings ???? and ???? are ?? ?? and ?? ?? respectively. The 
system is in equilibrium with a constant horizontal force ???? on ?? . The ?? ?? is 
(a) ???? 
(b) v?? ???? 
(c) v?? ???? 
(d) v?? ???? 
 
Ans: (b) From the free body diagram of block ?? 
 
?? 1
cos ?? 1
= ???? .
?? 1
sin ?? 1
= -???? .
 
by squaring and adding ?? 1
2
(sin
2
 ?? 1
+ cos
2
 ?? 1
)= 2(???? )
2
 
? ?? 1
= v2???? 
Q3: A block of mass ???? ???? is suspended through two light spring balances as 
shown in given Figure. 
(A) Both the scales will read ???? ???? 
(B) Both the scales will read ?? ???? . 
(C) The upper scales will read ???? ???? and the lower zero. 
(D) The readings may be anything but their sum will be ???? ???? 
Ans: (A) At point A; 
 
At point B; 
 
? Both the spring show a reading of 10 kg 
 
Q4: A block is kept on the floor of an elevator at rest. The elevator starts 
descending with an acceleration of ???? ?? /?? ?? . Find the displacement of the block 
during the first ?? .?? ?? after the start. Take ?? = ???? ?? /?? ?? . 
(A) ???? ???? 
(B) ???? ???? 
(C) ?? ?? ???? 
(D) ???? ???? 
Ans: (B) Here acceleration of the lift is 12 m/s
2
 which is greater than ' g '. 
at t = 0 
 
The body will undergo a free fall condition. Actually the body loses the contact with the 
floor of the lift. 
? s =
1
2
 gt
2
=
1
2
× 10(0.2)
2
 m
 S = 20 cm.
 
 
Q5: Two masses ?? and ?? ' are tied with a thread passing over a pulley. ?? '
 is on a 
frictionless horizontal surface and ?? is hanging freely. If acceleration due to 
Page 4


Solved Examples on Newton’s Laws 
of Motion 
 
JEE Mains 
Q1: Two forces are such that the sum of their magnitudes is ???? ?? and their 
resultant is perpendicular to the smaller force and magnitude of resultant is 12 . 
Then the magnitudes of the forces are 
(a)???? ?? ,?? ?? 
(b) ???? ?? ,?? ?? 
(c) ???? ?? ,?? ?? 
(d) 11N, 7N 
Ans: (b)  
 
Let two forces are ?? 1
 and ?? 2
(?? 1
< ?? 2
) . 
According to problem: ?? 1
+ ?? 2
= 18 
Angle between ?? 1
 and resultant (?? ) is 90
°
 
 ? tan 90 =
?? 2
sin ?? ?? 1
+ ?? 2
cos ?? = 8
 ? ?? 1
+ ?? 2
cos ?? = 0
 ? cos ?? = -
?? 1
?? 2
 and ?? 2
= ?? 1
2
+ ?? 2
2
+ 2?? 1
?? 2
cos ?? 144= ?? 1
2
+ ?? 2
2
+ 2?? 1
?? 2
cos ?? 
by solving (i), (ii) and (iii) we get ?? 1
= 5 N and ?? 2
= 13 N 
 
Q2: In the following figure the masses of the blocks ?? and ?? are same and each 
equal to ?? . The tensions in the strings ???? and ???? are ?? ?? and ?? ?? respectively. The 
system is in equilibrium with a constant horizontal force ???? on ?? . The ?? ?? is 
(a) ???? 
(b) v?? ???? 
(c) v?? ???? 
(d) v?? ???? 
 
Ans: (b) From the free body diagram of block ?? 
 
?? 1
cos ?? 1
= ???? .
?? 1
sin ?? 1
= -???? .
 
by squaring and adding ?? 1
2
(sin
2
 ?? 1
+ cos
2
 ?? 1
)= 2(???? )
2
 
? ?? 1
= v2???? 
Q3: A block of mass ???? ???? is suspended through two light spring balances as 
shown in given Figure. 
(A) Both the scales will read ???? ???? 
(B) Both the scales will read ?? ???? . 
(C) The upper scales will read ???? ???? and the lower zero. 
(D) The readings may be anything but their sum will be ???? ???? 
Ans: (A) At point A; 
 
At point B; 
 
? Both the spring show a reading of 10 kg 
 
Q4: A block is kept on the floor of an elevator at rest. The elevator starts 
descending with an acceleration of ???? ?? /?? ?? . Find the displacement of the block 
during the first ?? .?? ?? after the start. Take ?? = ???? ?? /?? ?? . 
(A) ???? ???? 
(B) ???? ???? 
(C) ?? ?? ???? 
(D) ???? ???? 
Ans: (B) Here acceleration of the lift is 12 m/s
2
 which is greater than ' g '. 
at t = 0 
 
The body will undergo a free fall condition. Actually the body loses the contact with the 
floor of the lift. 
? s =
1
2
 gt
2
=
1
2
× 10(0.2)
2
 m
 S = 20 cm.
 
 
Q5: Two masses ?? and ?? ' are tied with a thread passing over a pulley. ?? '
 is on a 
frictionless horizontal surface and ?? is hanging freely. If acceleration due to 
gravity is ?? , the acceleration of ?? '
 in this arrangement will be 
(A) ?? 
(B) ???? /(?? + ?? '
) 
(C) ???? /?? '
 
(D) ???? /(?? - ?? '
) 
Ans: (B) FBD of A; 
 
 
FBD of ?? ; 
 
Using (i) and (iii) 
mg= ma+ m
'
?? [(i)+ (iii)]
a = (
m
m+ m
'
)g
 
 
Q6: ?? body of mass ???? ???? is dragged with just enough force to start moving on a 
rough surface with coefficients of static and kinetic frictions 0.5 and 0.4 
respectively. On continuing (?? = ?? .?? ?? /?? ?? ) the same force what is the 
acceleration: 
(A) ?? .???? ?? /?? ?? 
(B) ?? .?? ?? /?? ?? 
(C) ?? .???? ?? /?? ?? 
(D) ?? .?????? ?? /?? ?? 
Ans: (A) Now, the force required to just start the motion would be the static friction (f
s
) 
Page 5


Solved Examples on Newton’s Laws 
of Motion 
 
JEE Mains 
Q1: Two forces are such that the sum of their magnitudes is ???? ?? and their 
resultant is perpendicular to the smaller force and magnitude of resultant is 12 . 
Then the magnitudes of the forces are 
(a)???? ?? ,?? ?? 
(b) ???? ?? ,?? ?? 
(c) ???? ?? ,?? ?? 
(d) 11N, 7N 
Ans: (b)  
 
Let two forces are ?? 1
 and ?? 2
(?? 1
< ?? 2
) . 
According to problem: ?? 1
+ ?? 2
= 18 
Angle between ?? 1
 and resultant (?? ) is 90
°
 
 ? tan 90 =
?? 2
sin ?? ?? 1
+ ?? 2
cos ?? = 8
 ? ?? 1
+ ?? 2
cos ?? = 0
 ? cos ?? = -
?? 1
?? 2
 and ?? 2
= ?? 1
2
+ ?? 2
2
+ 2?? 1
?? 2
cos ?? 144= ?? 1
2
+ ?? 2
2
+ 2?? 1
?? 2
cos ?? 
by solving (i), (ii) and (iii) we get ?? 1
= 5 N and ?? 2
= 13 N 
 
Q2: In the following figure the masses of the blocks ?? and ?? are same and each 
equal to ?? . The tensions in the strings ???? and ???? are ?? ?? and ?? ?? respectively. The 
system is in equilibrium with a constant horizontal force ???? on ?? . The ?? ?? is 
(a) ???? 
(b) v?? ???? 
(c) v?? ???? 
(d) v?? ???? 
 
Ans: (b) From the free body diagram of block ?? 
 
?? 1
cos ?? 1
= ???? .
?? 1
sin ?? 1
= -???? .
 
by squaring and adding ?? 1
2
(sin
2
 ?? 1
+ cos
2
 ?? 1
)= 2(???? )
2
 
? ?? 1
= v2???? 
Q3: A block of mass ???? ???? is suspended through two light spring balances as 
shown in given Figure. 
(A) Both the scales will read ???? ???? 
(B) Both the scales will read ?? ???? . 
(C) The upper scales will read ???? ???? and the lower zero. 
(D) The readings may be anything but their sum will be ???? ???? 
Ans: (A) At point A; 
 
At point B; 
 
? Both the spring show a reading of 10 kg 
 
Q4: A block is kept on the floor of an elevator at rest. The elevator starts 
descending with an acceleration of ???? ?? /?? ?? . Find the displacement of the block 
during the first ?? .?? ?? after the start. Take ?? = ???? ?? /?? ?? . 
(A) ???? ???? 
(B) ???? ???? 
(C) ?? ?? ???? 
(D) ???? ???? 
Ans: (B) Here acceleration of the lift is 12 m/s
2
 which is greater than ' g '. 
at t = 0 
 
The body will undergo a free fall condition. Actually the body loses the contact with the 
floor of the lift. 
? s =
1
2
 gt
2
=
1
2
× 10(0.2)
2
 m
 S = 20 cm.
 
 
Q5: Two masses ?? and ?? ' are tied with a thread passing over a pulley. ?? '
 is on a 
frictionless horizontal surface and ?? is hanging freely. If acceleration due to 
gravity is ?? , the acceleration of ?? '
 in this arrangement will be 
(A) ?? 
(B) ???? /(?? + ?? '
) 
(C) ???? /?? '
 
(D) ???? /(?? - ?? '
) 
Ans: (B) FBD of A; 
 
 
FBD of ?? ; 
 
Using (i) and (iii) 
mg= ma+ m
'
?? [(i)+ (iii)]
a = (
m
m+ m
'
)g
 
 
Q6: ?? body of mass ???? ???? is dragged with just enough force to start moving on a 
rough surface with coefficients of static and kinetic frictions 0.5 and 0.4 
respectively. On continuing (?? = ?? .?? ?? /?? ?? ) the same force what is the 
acceleration: 
(A) ?? .???? ?? /?? ?? 
(B) ?? .?? ?? /?? ?? 
(C) ?? .???? ?? /?? ?? 
(D) ?? .?????? ?? /?? ?? 
Ans: (A) Now, the force required to just start the motion would be the static friction (f
s
) 
 
? F = f
s
= ?? ?? mg 
i.e. after this point the body starts moving. 
When the body is moving, kinetic friction acts on the body (i. e ?? k
mg ) 
FBD of the body; 
 
F - f
k
= ma
 ?? 5
mg- ?? k
mg= ma
 ? (?? s
- ?? k
)mg= ma ? a = (?? s
- ?? k
)g
a = 0.98 m/s
2
 
 
Q7: Which of the following represents ?? nd 
 law of motion most correctly. 
(A) ?? ? ? 
= ?? ??? ?  
(B) ?? ? ? 
= ?? ?? ??? ? 
????
 
(C) ?? 
=
?? ??? ? 
????
 
(D) ?? ? ? 
= ?? ?? ? ? 
 
Ans: (C) Newton's second law states that the net force on an object is equal to the rate 
of change of its linear momentum. 
? ?? 
=
?? ?? 
????
=
?? (?? ?? )
????
 
if m is constant, then 
= m·
dv ? 
dt
= ma 
 
Q8: Two objects A and B are thrown upward simultaneously with the same speed. 
The mass of ?? is greater than the mass of ?? . Suppose the air exerts a constant 
and equal force of resistance on the two bodies. 
(A) The two bodies will reach the same height. 
(B) A will go higher than ?? 
(C) B will go higher than ?? 
(D) Any of the above three may happen depending on the speed with which the 
objects are thrown.