Constraint Motion (WS)

TM
Path to success
KOTA (RAJASTHAN )
WORKSHEET
JEE (MAIN+ADVANCED) 2016
CONSTRAINT MOTION
NURTURE COURSE
PHYSICS
BATCH : UAY, W1X, VAZ
1.
Two blocks are arranged as shown in the figure. The relation
between acceleration a1 and a2 is :
(A) a1 = a2
(B*) a1 = 6a2
(C) a1 = 3a2
(D) a1 = 4a2
2.
In the given figure find the velocity and acceleration of B, if velocity and
acceleration of A are as shown.
3.
The three blocks shown move with constant velocities. Find the velocity
of block A and B. Given VP2=10m/s, Vc=2m/s .
4.
For the system shown, calculate velocity and acceleration of C.The velocity
and acclerations of A and B with respect to ground are marked.
5.
The pulley moves up with a velocity of 10m/sec. Two blocks are tied by a
string which passes over a pulley. The velocity V will be _________.
Given: vB = 5m/s
6.
Slider block A move to the left with a constant velocity of 6 m/s. Determine
(a) the velocity of block b,
(b) the velocity of portion D of the cable.
(c) the relative velocity of portion C of the cable with respect to portion D.
7.
In the arrangement shown, all surfaces are frictionless. The rod R is constrained to
move vertically. The vertical acceleration of R is a 1 and the horizontal acceleration
of the wedge W is a2. The ratio a1
(A) sin 
(C*) tan 
8.
a 2 is equal to
(B) cos 
(D) cot 
System is shown in the figure and man is pulling the rope from both sides with
constant speed ‘u’. Then the velocity of the block will be
3u
4
u
(C)
4
(A*)
PHYSICS
(B)
3u
2
(D) None
1
9.
System is shown in figure and wedge is moving towards left with speed 2 m/
s. Then velocity of the block B will be
(A) 3 m/s
(C*) 2 m/s
10.
(B) 1 m/s
(D) 4 m/s
In the figure shown, the speed of the truck is v to the right. The speed with
which the block is moving up at  = 60° is :
(A) v
(C*)
(B)
3v 4
2v 3
(D) none
11.
Determine the relationship that governs the velocity of four cylinder
velocities as positive down.
12.
Determine the speed with which block B rises in figure if the end of the cord
at A is pulled down with a speed of 2 m/s.
13.
If acceleration of wedge = 5 m/s2 to the right. Find the magnitude of
acceleration of the block B. The string is inextensible
14.
If the strings is inextensible, determine the velocity u of each block in terms of v and .
(i) Fig. (A) u = _________.
15.
(ii) Fig. (B)
u = _________.
The system is in equilibrium
(a) Draw FBD of 10 kg block.
(b) Draw FBD of 5 kg wedge.
(c) Find "F" so that the system is in equilibrium
Neglect friction
16.
A balloon is tied to a block. The mass of the block is 2 kg. The tension of the
string between the balloon and the block is 30 N. Due to the wind the string has
an angle  relative to the vertical direction. cos  = 4/5 and sin  = 3/5.
Assume the acceleration of gravity is g = 10 m/s2. Also assume the block is small
so the force on the block
from the wind can be ignored.
PHYSICS
2
Find the x-component and the y-component of the force F exerted on the block by the string.
(b)
Find the x-component and the y-component of the acceleration a of the block.
Assume the mass of the balloon is zero and the force of the wind on the balloon is in the x-direction. Find
the magnitude of the force of the wind on the balloon.
(c)
17.

(a)

One end of a light inextensible string is attached to a ceiling. The string passes
under a smooth light pulley carrying a weight C and then over a fixed smooth
light pulley. To the free end of the string is attached a light scale pan in which two
weights A and B are placed with A on top of B as shown. The portions of the
string not in contact with the pulleys are vertical. Each of the weights A and B
has a mass M and the weight C has a mass 5M. If the system is released from
rest
(a) find the acceleration of the movable pulley?
(b) the tension in the string.
(c) the reaction force between the weights A and B.
18.
To point the side of a building, painter normally hoists himself up by pulling on
the rope A as in figure. The painter and platform together weigh 200N. The rope
B can withstand 300N. Find
(a) the maximum acceleration of the painter.
(b) tension in rope A
(i) when painter is at rest
(ii) when painter moves up with an acceleration 2 m/s 2.
19.
Three blocks A, B & C are arranged as shown. Pulleys and strings are ideal. All surfaces are frictionless. If block
C is observed moving down along the incline at 1 m/s2. Find mass of block B, tension in string and accelerations
of A, B as the system is released from rest.
ANSWERS
1. (B)
4. Vc = 4m/s, aC = 5m/s2
7. (C)
10. (C)
2. vB = 0.5 m/s & aB = 1 m/s2 
5. 25m/s
8. (A)
11. 4vA + 8vB + 4vC + vD = 0]
13. 5 m/s2
14. (i)
15. (a)
(b)
3. vA=10m/s, vB=22m/s
6. (a) 2 m/s , (b) 2 m/s , (c) 8 m/s 
9. (C)
12. 0.5 m/s 
v
v
, (ii)
2 cos
cos
(c) 75 N
16. (a) Tx = 18 N, Ty = 24 N ; (b) ax = 9 m/s2, ay = 2 m/s2; (c) Fwind = 18 N
17. (a)
g
30Mg
15Mg
(b)
(c)
13
13
13
18. (a) 5m/s2, (b)(i)100 N, (ii) 120 N
PHYSICS
19. MB = 15 kg, T = 15 , aA = 5 m/s2 , aB = 9 m/s2 ]
3

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