Laws of Motion Vardan Patni’s Physics Classes (9584120300)
Section – 1: Find force/tension and acceleration for the following cases.
Question Force/ Tension & Acceleration
1
Laws of Motion Vardan Patni’s Physics Classes (9584120300)
2
Laws of Motion Vardan Patni’s Physics Classes (9584120300)
10
11
3
Laws of Motion Vardan Patni’s Physics Classes (9584120300)
12
13
14
4
Laws of Motion Vardan Patni’s Physics Classes (9584120300)
Section - 2
1. Two blocks of masses 7 𝑘𝑔 and 5 𝑘𝑔 are 4. Two blocks 𝐴 and 𝐵 each of mass 𝑚 are
placed in contact with each other on a placed on a smooth horizontal surface. Two
smooth surface. If a force of 6 𝑁 is applied on horizontal forces 𝐹 and 2𝐹 are applied on the
the heavier mass, the force on the lighter blocks 𝐴 and 𝐵 respectively as shown in
mass is figure. The block 𝐴 does not slide on block 𝐵.
Then, the normal reaction acting between the
two blocks is
a. 3.5 𝑁
b. 2.5 𝑁
c. 7 𝑁
d. 5 𝑁 a. 𝐹
𝐹
2. Three blocks of mass 4 𝑘𝑔, 2 𝑘𝑔, 1 𝑘𝑔 b. 2
respectively are in contact on a frictionless c.
𝐹
table as shown in the figure. If a force of 14 𝑁 √3
d. 3𝐹
is applied on the 4 𝑘𝑔 block, the contact force
5. Find the force of interaction between the
between the 4 𝑘𝑔 and the 2 𝑘𝑔 block will be
bodies as shown in figure. Blocks are in
contact.
a. 2 𝑁
b. 6 𝑁
c. 8 𝑁 6. Three blocks, of masses 𝑚1 = 2.0, 𝑚2 = 4.0
d. 14 𝑁 and 𝑚3 = 6.0 𝑘𝑔 are connected by strings on
3. Two blocks of masses 1 𝑘𝑔 and 2 𝑘𝑔 are a frictionless inclined plane of 60°, as shown
placed in contact on a smooth horizontal in figure. A force 𝐹 = 120 𝑁 is applied
surface as shown in figure 1 and 2. A upward along the incline to the uppermost
horizontal force of 6 𝑁 is applied first on 1 𝑘𝑔 block, causing an upward movement of the
block and then on 2 𝑘𝑔 block. The force of blocks. The connecting cords are light. The
interaction of the blocks in both the cases, values of tensions 𝑇1 and T2 in the cords are
respectively are
a. 4 𝑁, 2 𝑁
b. 8 𝑁, 4 𝑁
c. 2 𝑁, 1 𝑁 a. T1 = 20 𝑁, T2 = 60 𝑁
d. 6 𝑁, 3 𝑁 b. T1 = 60 𝑁, T2 = 60 𝑁
c. T1 = 30 𝑁, T2 = 50 𝑁
d. T1 = 20 𝑁, T2 = 100 𝑁
5
Laws of Motion Vardan Patni’s Physics Classes (9584120300)
7. Three blocks of masses 𝑚1 , 𝑚2 and 𝑚3 are 11. The blocks of masses 2 𝑘𝑔, 3 𝑘𝑔 and 5 𝑘𝑔 are
connected by massless strings as shown on a connected by light, inextensible strings as
frictionless table. They are pulled with a force shown. The system of blocks is raised
𝑇3 = 40 𝑁. If 𝑚1 = 10 𝑘𝑔, 𝑚2 = 6 𝑘𝑔 and vertically upwards by applying a force
𝑚3 = 4 𝑘𝑔, the tension T2 will be 𝐹0 = 200 𝑁. The common acceleration and
tensions in the strings are
a. 20 𝑁
b. 40 𝑁
c. 10 𝑁
d. 32 𝑁
8. Two bodies 𝐴 and 𝐵 of masses 10 𝑘𝑔 and
15 𝑘𝑔 respectively kept on a smooth,
horizontal surface are tied to the ends of a
light string. If 𝑇 represents the tension in the
string when a horizontal force 𝐹 = 500 𝑁 is
applied to 𝐴 as shown in figure-1 and 𝑇′ be 𝑚
a. 𝑎 = 5 𝑠2 , 𝑇1 = 120 𝑁, 𝑇2 = 80 𝑁
the tension when it is applied to 𝐵 as shown 𝑚
in figure-2, then which of the following is true b. 𝑎 = 10 , 𝑇1 = 160 𝑁, 𝑇2 = 100 𝑁
𝑠2
𝑚
c. 𝑎 = 20 𝑠2 , 𝑇1 = 180 𝑁, 𝑇2 = 120 𝑁
𝑚
d. 𝑎 = 10 2 , 𝑇1 = 100 𝑁, 𝑇2 = 50 𝑁
𝑠
12. Three blocks with masses 𝑚, 2𝑚 and 3𝑚 are
connected by strings, as shown in figure. After
an upward force 𝐹 is applied on block 𝑚, the
masses move upward at constant speed 𝑣.
What is the net force on the block of mass 2𝑚
a. 𝑇 = 𝑇’ = 500 𝑁
b. 𝑇 = 𝑇’ = 250 𝑁
c. 𝑇 = 200 𝑁, 𝑇’ = 300 𝑁
d. 𝑇 = 300 𝑁, 𝑇’ = 200 𝑁
9. Three blocks 𝐴, 𝐵 and 𝐶 each of mass 2 𝑘𝑔,
are hanging over a fixed pully as shown. The
tension in the string
connecting 𝐵 and 𝐶 is
a. 0
b. 3.3 𝑁
c. 13.3 𝑁
d. 19.6 𝑁 a. 6 𝑚𝑔
b. 0
10. A body of weight 200 𝑁 is suspended from a c. 2 𝑚𝑔
tree branch through a chain of mass 10 𝑘𝑔. d. 3 𝑚𝑔
The branch pulls the chain by a force equal to
a. 100 𝑁
b. 150 𝑁
c. 200 𝑁
d. 300 𝑁
6
Laws of Motion Vardan Patni’s Physics Classes (9584120300)
13. Two blocks of masses 3 𝑘𝑔 and 6 𝑘𝑔 are 18. The pulleys and strings shown in the figure
connected by a string as shown in the figure are smooth and of negligible mass. For the
over a frictionless pulley. The acceleration of system to remain in equilibrium, the angle 𝜃
the system is should be
𝑚
a. 4 𝑠2
𝑚 a. 0°
b. 2 𝑠2 b. 30°
c. 0 c. 45°
𝑚
d. 6 𝑠2 d. 60°
19. A block 𝐴 of mass 7 𝑘𝑔 is placed on a
14. The acceleration of system over the wedge as frictionless table. A thread tied to it passes
shown in the figure is over a frictionless pulley and carries a body 𝐵
of mass 3 𝑘𝑔 at the other end. The
𝑚
a. 1 acceleration of the system is
𝑠2
𝑚
b. 2 𝑠2
𝑚
c. 3
𝑠2
𝑚
d. 4 𝑠2
15. A block of √3 𝑘𝑔 is attached to a string whose
other end is attached to the wall. An unknown
force 𝐹 is applied so that the string makes an
angle of 30° with the 𝑚
a. 100 𝑠2
wall. The tension 𝑇 is 𝑚
b. 3 𝑠2
(Given 𝑔 = 10 𝑚/𝑠 2 ) 𝑚
c. 10
𝑠2
𝑚
a. 20 𝑁 d. 30 2
𝑠
b. 25 𝑁 20. Two bodies of mass 4 𝑘𝑔 and 6 𝑘𝑔 are tied to
c. 10 𝑁 the ends of a massless string. The string
d. 15 𝑁
passes over a pulley which is frictionless. The
16. A string of negligible mass going over a
acceleration of the system in terms of
clamped pully of mass 𝑚 supports a block of
acceleration due to gravity 𝑔 is
Mass 𝑀 as shown in the figure. The force on
the pulley by the clamp is given
by
a. √2 𝑀𝑔
b. √2 𝑚𝑔
c. √(𝑀 + 𝑚)2 + 𝑚2 𝑔
d. 𝑔√(𝑀 + 𝑚)2 + 𝑀2
𝑔
a. 2
𝑔
17. The acceleration of the block b.
5
𝐴 is 𝑔
2𝑔
c. 10
a. upward
3 d. 𝑔
𝑔
b. 3
upward
2𝑔
c. 3
downward
𝑔
d. downward
3
7
Laws of Motion Vardan Patni’s Physics Classes (9584120300)
21. In the arrangement shown in figure the ends 24. A body of mass 1 𝑘𝑔 is suspended with the
𝑃 and 𝑄 of an unstretchable string move help of two strings making angles as shown in
downwards with uniform speed 𝑢. Pulley 𝐴 figure. Magnitudes of tensions 𝑇1 and 𝑇2 ,
and 𝐵 are fixed. Mass 𝑀 moves upwards with respectively, are (in 𝑁)
a speed
a. 5√3, 5
b. 5, 5√3
a. 2𝑢 cos 𝜃 c. 5, 5
b. 𝑢 cos 𝜃 d. 5√3, 5√3
2𝑢
c. cos 𝜃 25. A 1 𝑘𝑔 mass is suspended from the ceiling by
d.
𝑢 a rope of length 4 𝑚. a horizontal force 𝐹 is
cos 𝜃 applied at the mid-point of the rope, so that
22. The acceleration of 𝑚 is
the rope makes an angle of 45° with respect
to the vertical axis
as shown in figure.
The magnitude of
𝐹 is
1
a. 10√2
𝑁
b. 1 𝑁
𝑔
c. 10 𝑁
a. up the plane 10
3 d. 𝑁
𝑔 √2
b. 3
down the plane 26. The monkey 𝐵 shown in figure is holding on to
2𝑔
c. up the plane the tail of the monkey 𝐴 which is climbing up
3
2𝑔 a rope. The masses of the monkeys 𝐴 and 𝐵
d. 3
down the plane
are 5 𝑘𝑔 and 2 𝑘𝑔 respectively. If 𝐴 can
23. A body of mass 𝑚 is suspended by two strings
tolerate a tension of 30 𝑁 in its tail, what
making angles 𝜃1 and 𝜃2 with the horizontal
force should it apply on the rope in order to
ceiling with tensions 𝑇1 and 𝑇2
carry the monkey 𝐵
simultaneously. 𝑇1 and 𝑇2 are related by
with it.
𝑇1 = √3𝑇2 , the angles 𝜃1 and 𝜃2 are a. 20 𝑁
3𝑚𝑔
a. 𝜃1 = 30°, 𝜃2 = 60° with 𝑇2 = 4
b. 50 𝑁
b. 𝜃1 = 30°, 𝜃2 = 60° with 𝑇2 =
4𝑚𝑔 c. 70 𝑁
5
𝑚𝑔 d. 100 𝑁
c. 𝜃1 = 60°, 𝜃2 = 30° with 𝑇2 = 2
3𝑚𝑔
d. 𝜃1 = 45°, 𝜃2 = 45° with 𝑇2 =
4
8
Laws of Motion Vardan Patni’s Physics Classes (9584120300)
Section - 1
𝐹 𝑚2 𝐹
1. 𝑎 = ,𝑅 =
𝑚1 +𝑚2 𝑚1 +𝑚2
𝐹 𝑚1 𝐹
2. 𝑎 = 𝑚1 +𝑚2
, 𝑅 = 𝑚 +𝑚
1 2
𝐹 (𝑚2 +𝑚3 )𝐹 𝑚 𝐹
3. 𝑎 = 𝑚1 +𝑚2 +𝑚3
, 𝑅1 = 𝑚 +𝑚 +𝑚 , 𝑅2 = 𝑚 +𝑚3 +𝑚
1 2 3 1 2 3
𝐹 𝑚1 𝐹
4. 𝑎 = 𝑚1 +𝑚2
, 𝑇 = 𝑚1 +𝑚2
𝐹 𝑚2 𝐹
5. 𝑎 = ,𝑇 =
𝑚1 +𝑚2 𝑚1 +𝑚2
𝐹 𝑚 𝐹 (𝑚1 +𝑚2 )𝐹
6. 𝑎 = 𝑚1 +𝑚2 +𝑚3
, 𝑇1 = 𝑚 +𝑚1 +𝑚 , 𝑇2 = 𝑚 +𝑚
1 2 3 1 2 +𝑚3
𝐹 (𝑚2 +𝑚3 )𝐹 𝑚3 𝐹
7. 𝑎 = 𝑚 +𝑚 +𝑚
, 𝑇1 = 𝑚 +𝑚 +𝑚 , 𝑇2 = 𝑚 +𝑚 +𝑚
1 2 3 1 2 3 1 2 3
2𝑚1 𝑚2 4𝑚1 𝑚2 𝑚 −𝑚
8. 𝑇1 = (𝑚 +𝑚 )
𝑔 , 𝑇2 = (𝑚 +𝑚 )
𝑔, 𝑎 = [𝑚2 +𝑚1 ] 𝑔
1 2 1 2 1 2
2𝑚1 (𝑚2 +𝑚3 ) 2𝑚1 𝑚3 4𝑚 (𝑚 +𝑚 ) [(𝑚2 +𝑚3 )−𝑚1 ]
9. 𝑇1 = 𝑚 +𝑚 +𝑚 𝑔 , 𝑇2 = 𝑚 +𝑚 +𝑚 𝑔 , 𝑇1 = 𝑚 1+𝑚2 +𝑚3 𝑔, 𝑎 = 𝑚1 +𝑚2 +𝑚3
𝑔
1 2 3 1 2 3 1 2 3
𝑚2 𝑚 𝑚
10. 𝑎 = 𝑚 +𝑚 𝑔, 𝑇 = 𝑚 1+𝑚2 𝑔
1 2 1 2
𝑚 −𝑚1 sin 𝜃 𝑚 𝑚 (1+sin 𝜃)
11. 𝑎 = [ 2𝑚 +𝑚 ] 𝑔, 𝑇 = 1 𝑚2 +𝑚 𝑔
1 2 1 2
𝑚 sin 𝛽−𝑚 sin 𝛼 𝑚 𝑚 (sin 𝛼+sin 𝛽)
12. 𝑎 = [ 2 𝑚 +𝑚1 ] 𝑔, 𝑇 = 1 2𝑚 +𝑚 𝑔
1 2 1 2
𝑚 𝑔 sin 𝜃 2𝑚1 𝑚2
13. 𝑎= 1 ,𝑇= 𝑔 sin 𝜃
𝑚1 +𝑚2 4𝑚1 +𝑚2
2𝑚2 𝑔 𝑚 𝑔 2𝑚 𝑚
14. 𝑎1 = 4𝑚 +𝑚 , 𝑎2 = 4𝑚 2+𝑚 , 𝑇 = 4𝑚 1+𝑚2 𝑔
1 2 1 2 1 2
Section - 2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
B B A D - A D C C D B B C A A D C C B B
21 22 23 24 25 26
D A C A C C
𝐹 cos 𝜃 𝐹 cos 𝜃
5. 𝑅1 = 𝑚1 (𝑚 ), 𝑅2 = (𝑚1 + 𝑚2 ) (𝑚 )
1 +𝑚2 +𝑚3 1 +𝑚2 +𝑚3
