CASE 05 Mass suspended over a pulley from another on an
inclined plane.
N a
T
m2 T
a
m2gCos m1
m2gSin
m 2g
For mass m1 ; m 1g
m1g – T = m1a
For mass m2 ;
T – m2gSin = m2a
(m1 − m2Sin)
a= g
(m1 + m2)
N a
T
m2 T
m2gCos m1
m2gSin
m1g – T = m1a
m 2g
m 1g
T2 – m2gSin = m2a
m1m2(1 + sinθ)
T= g
(m1 + m2)
CASE 06
For mass m1 ;
T1 – m1g = m1a
T1 T1
For mass m2 ;
m2g + (T2 – T1) = m2a a
a m1
For mass m3 ;
m2
m3g - T2= m3a m 1g
m 2g
T2
(m2 + m3 − m1)
a= g
(m1 + m2 + m3)
m3
Using the above equations we can get the values of
T1 and T2. m 3g
Question
Two masses M and M/2 are joint together by
means of a light inextensible string passes over
a frictionless pulley as shown in figure. When
bigger mass is released the small one will a
a
ascend with an acceleration of
(A) g/3 T T
(B) 3g/2
(C) g
(D) g/2
M/2
Question
Ans: (a) g/3
Question
Two blocks, weighing 250N and 350 N, respectively, are
connected by a string that passes over a massless pulley as
shown. The tension in the string is:
(A) 180.7 N
(B) 207.33 N
(C) 291.66 N
(D) 350 N
a a
T T
250 N
350 N
Question
Ans: (C) 291.66 N
Question
Three equal weights A, B and C of mass 2 kg
each are hanging on a string passing over a
fixed frictionless pulley as shown in the
figure. The tension in the string connecting
weights B and C is T1 T1
A
B
T2
C
Question
Ans: 13 N
Numerical Practice
Question
A block of mass 20 kg is raised by a 55 kg man in two different
ways as shown in fig. What is the action on the floor by the man
in the two cases? If the floor yields to a normal force of 700 N,
which mode should be the man adopt to lift the block without the
floor yielding?
F
Mg
Mg
F (a)
(b)
mg
mg
Solution
F
Mg
Mg
F (a)
(b)
mg
mg
Solution
F
Mg
Mg
F (a)
(b)
mg
mg
Ans: 735 N and 343 N
The mode (b) Should be adopted
by the man to lift block.
Question
A 70-N block and a 35-N block are connected by a string as
shown. If the pulley is massless and the surface is frictionless, the
magnitude of the acceleration of the 35-N block is:
(A) 3 m/s2
(B) 3.27 m/s2
70 N
(C) 4 m/s2
(D) 6.2 m/s2
35 N
Solution
70 N
35 N
Ans: (B) 3.27 m/s2
Question
Two masses 8 Kg and 12 Kg are connected at the two ends of a
light inextensible string that goes over a frictionless pulley. Find
the acceleration of the masses, and the tension in the string
when the masses are released.
a a
T T
8 Kg
12 Kg
Solution
a a
T T
8 Kg
12 Kg
Solution
a a
T T
8 Kg
12 Kg
Ans: 2 m/s2, 96 N
Question
A block A of mass 7 kg is placed on a frictionless table. A thread
tied to it passes over a frictionless pulley and carries a body B of
mass 3 kg at the other end. The acceleration of the system is
(given g = 10 ms–2)
(A) 100ms−2 A
(B) 3ms−2
(C) 10ms−2 B
(D) 30ms −2
Solution
A
Ans: (B)
Question
A girl is using a rope to pull a box that weighs 300 N across a
level surface with constant velocity. The rope makes an angle of
30° above the horizontal, and the tension in the rope is 100 N.
What is the normal force of the floor on the box?
(A) 300 N (B) 86 N (C) 50 N (D) 250 N
Solution
Ans: (D)
Homework
Question
A 10-kg mass and a 2.0-kg mass are connected by a light string
over a massless, frictionless pulley. If g = 9.8 m/s2, what is the
acceleration of the system when released?
a a
T T
2Kg
10 Kg
Ans: 6.5 m/s2
Question
Two masses of 4 kg and 5 kg are connected by a string passing
through a frictionless pulley and are kept on a frictionless table
as shown in the figure. The acceleration of 5 kg mass is
4 kg
5 kg
Ans: 5.44 m/s2
Question
The system shown remains at rest. Each block weighs 20 N. The
force of friction on the upper block is: W = 20 N
a =3m
b =4m
W
a W
Ans: 8 N
