An engineer is designing a conveyor system for loading lay bales into a wagon. Each bale is 0.25 m. wide, 0.50 m high, and 0.80 m long (the dimension perpendicular to the plane of the figure), with mass 30.0 Kg. The center of gravity of each bale is at its geometrical center. The coefficient of static friction between a bale and the conveyor belt is 0.60, and the belt moves with constant
speed. The angle β of the conveyor is slowly increased. At some critical angle a bale will tip (if it doesn't slip first), and at some different critical angle it will slip (if it doesn't tip first).
1. Find the first critical angle (In the same conditions) at which it tips
A) β = tan-1 0.50 B) β = tan-1 0.60 C) β = tan-1 0.40 D) β = tan-1 0.20
2. Find the second critical angle (in the same conditions) at which it slips.
A) β = tan-1 0.50 B) β = tan-1 0.60 C) β = tan-1 0.12 D) β = tan-1 0.70
3. Find the first critical angle at which it tips if the coefficient of friction were 0.40 ? A) β = tan-1 0.50 B) β = tan-1 0.60 C) β = tan-1 0.70 D) β = tan-1 0.20
4. Find the second critical angle at which it slips if the coefficient of friction were 0.40 ? A) β = tan-1 0.50 B) β = tan-1 0.60 C) β = tan-1 0.40 D) β = tan-1 0.70
5. Which statement/s is/are correct
A) At smaller angle it will tip first if µs = 0.60 B) At smaller angle it will tip first if µ s = 0.40 C) At larger angle it will tip first if µ s = 0.60 D) At larger angle it will tip first if µ s = 0.40 Passage II: (Q.No: 6 to 10):
A moving company uses the pulley system in figure 1 to lift heavy crates up a ramp. The ramp is coated with rollers that make the crate's motion essentially frictionless. A worker piles cinder blocks onto the plate until the plate moves down, pulling the crate up the
ramp. Each cinder block has mass 10 kg. The plate has mass 5 kg. The rope is nearly massless, and the pulley is essentially frictionless. The ramp makes a 300 angle with the ground. The crate has mass 100 kg.
Let W1 denote the combined weight of the plate and the cinder blocks piled on the plate. Let T denote the tension in the rope. And let W2 denote the crate's weight. 6. What is the smallest number of cinder blocks that need to be placed on the plate in
order to lift the crate up the ramp ?
A) 3 B) 5 C) 7 D) 10
7. Ten cinder blocks are placed on the plate. As a result, the crate accelerates up the ramp. Which of the following is true ?
A) W1 = T = W2 sin 300 B) W1 = T > W2 sin 300 C) W1 > T = W2 sin 300 D) W1 > T > W2 sin 300
8. The ramp exerts a "normal" foce on the crate, directed perpendicular to the ramp's surface. This normal force has magnitude.
A) W2 B) W2 sin 300 C) W2 cos 300 D) W2 (sin 300 + cos 300)
9. The net force on the crate has magnitude.
A) W1 - W2 sin 300 B) W1 - W2 C) T - W2 sin 300 D) T - W2 10. After the crate is already moving, the cinder blocks suddenly fall off the plate.
Which of the following graphs best shows the subsequent velocity of the crate, after the cinder blocks have fallen off the plate ? (up-the-ramp is the positive direction)
PASSAGE - III (Q.No: 11 to 16):
Two physics student were going to appear at the International Physics Olympiad, scheduled to start at 11.00 a.m. They left for the examination centre on a car in the morning at 8.00 a.m. It is being known to them that during the complete journey the car accelerates or decelerates at the same constant rate. Both of them decided to verify some of the concepts of physics on the way. They
are having a light string and two identical small balls, say B1 and B2, each of mass 'm'. In the car Joe sits on the left end and Becky sits on the right end with a separation of 1 metre between them, as shown in the figure. Joe ties the ball B1 with the string whose one end is fixed to the ceiling of the car as shown. At 9:30 a.m. Joe notices the string attached to the ball B1 to be inclined with the vertical towards Becky. At the same instant Becky throws the ball B2 vertically upward with respect to herself such that it does not touch the ceiling of the car. Again at 10:15 a.m. when the car was heading towards the examination centre, Joe finds that the string, which was vertical, has just started deflecting from the vertical. He quickly cuts the string and finds that the ball lands in Becky's hards!.
11. At 9:30 a.m. the tension in the string is:
A) equal to (mg) B) greater than (mg) C) less than (mg) D) needs more information
12. At 9:30 a.m., the car is :
A) moving with uniform velocity B) accelerating
C) decelerating D) temporarily at rest
13. The ball B2 will :
A) fall in hands of Becky B) fall infront of Becky
C) fall behind Becky D) land depending upon the speed of car
14. The magnitude of acceleration or retardation of car is :
A) 8 m/s2 B) 4 m/s2 C) 2 m/s2 D) 1 m/s2
15. The path of ball B1, after being separated from the cut string, as observed by Becky is :
A) Circle B) Straight line C) Parabola D) Ellipse
16. As observed by Becky the acceleration of ball 'B1' after the string is cut, will be: A) equal to 'g' B) greater than 'g' C) less than 'g' D) zero
Passage - IV (Q.No: 17 to 21):
A sufficiently long plank of mass 4 kg is placed on a smooth horizontal surface. A small block of mass 2 kg is placed over the plank and is being acted upon by a time varying horizontal force F = (0.5t), where 'F' is in Newton and 't' is in second as shown in fig. (a). The coefficient of friction between the plank and the block is given as
µ
s =µ
k =µ
. At time t = 12 sec, the relative slipping between the plank and theblock is just likely to occur.
If the force F acting on 2 kg block is removed and the system (plank + block) is given horizontal velocity 'V0, as shown in fig. (b), this system strikes a mass less spring of spring constant k = 120 N/m fixed at the end of the relative slipping occurs between the plank and the block.
17. The coefficient of friction
µ
is equal to :A) 0.10 B) 0.15 C) 0.20 D) 0.30
18. The acceleration (a) versus time (t) graph for the plank and the block shown in figure (a) is correctly represented in :
19. The average acceleration of the plank in the time interval 0 to 15 sec. in fig. (a) will be:
A) 0.20 m/s2 B) 0.30 m/s2 C) 0.40 m/s2 D) 0.60 m/s2
20. The magnitude of frictional force ' fr ' developed on 2 kg block versus compression 'x' of the spring from its natural length, as in fig. (b), is best represented in:
A) B) C) D)
21. The maximum possible value of 'V0', as in fig. (B), upto which no relative slipping occurs between the plank and the block will be:
A) 0.10m /s B) 0.20m /s C) 0.30m /s D) 0.40m /s Passage - V (Q.No: 22 to 26)
A physicist decided to find the friction coefficient between a plank and a block. His experimental setup is as shown in the above figure through which he could determine the coefficient of static friction and coefficient of kinetic friction, i.e.,
µ
s andµ
k, between the plank AB and theblock. The length of the plank is measured to be 4 metres and the mass of the block is 'M'.
The block is first placed on the plank and then plank is slowly inclined. When the height 'h', as shown in figure, becomes 2 metre, the relative slipping between the block and the plank is just likely to occur. Now this height 'h' is further increased to 2.4 metres and then the block is released from rest at the position 'B' and the time taken by the block to reach the position 'A' is measured to be 2 seconds by a stop- watch.
22. The friction coefficients,
µ
s andµ
k, are:A)
µ
s=
( )
1/
3
andµ
k = 0.5 B)µ
s=
3
andµ
k =0.5C)
µ
s=
( )
1/
3
andµ
k = 0.6 D)µ
s = 0.75 andµ
k =0.523. The variation of frictional force
( )f
r,
between the block and the plank, versus angle( )θ
made by the plank with horizontal is correctly represented in :24. When h = 2.4 m, the block is projected from position A with a velocity of 10m/s up the plane. The velocity of the block when it reaches to position B will be:
A) zero B) 2 5m/s C) 2 13 m/s D) won't
reach B
25. If h = 1 m, then the frictional force applied by the surface of plank on the block will be:
A) mg B) 0.5 mg C) 0.6 mg D) 0.25 mg
26. If h = 2.4 m, and a force 'F' is applied on the block parallel to the plane of the plank, then the range of the force 'F' for which the block will remain in equilibrium is given by: A) + ≤ ≤ 3 80 . 0 60 . 0 0 F mg B) − ≤ ≤ 3 80 . 0 60 . 0 F 0 mg A) B) C) D)
C) mg F mg + ≤ ≤ − 3 80 . 0 60 . 0 3 80 . 0 60 . 0 D) (0.60)mg≤ F ≤(0.80)mg Passage - VI (Q.No: 27 to 29)
In a monkey family three naughty monkeys A, B and C of masses mA, mB and mC respectively lived together. On a bright sunny day they were playing together. A rough light rope was hanging from a smooth branch of a tree as shown in the figure. Firstly, monkey B was holding one end of the rope and sat on the ground. Monkey A was holding the other end of the rope and was swinging in the air. During
the oscillatory motion of monkey A, the monkey B always remained in equilibrium touching the ground. After monkey A stops swinging, the monkey B releases the rope and sits on the ground at some distance from the rope and this end of the rope was now tightly held by monkey C. As the monkey A climbed up the rope with some acceleration, the monkey C was lifted up and always remained at the same level as that of monkey A. Doing so when monkeys A and C reached on to the branch of the tree the monkey B threw an apple directly aiming at A with sufficient velocity. At the very instant the monkey B threw the apple, the monkey A just released the branch of the tree to catch up the apple, in temptation.
27. The masses of monkeys A, B and C are correctly related in :
A) mA =mB =mC B) mA =mC >mB C) mA <mC <mB D) B
C
A m m
m = <
28. The force applied by the ground on the monkey B during the oscillatory motion of monkey A:
A) is minimum when A is at extreme position B) is minimum when A is at half of extreme position C) is minimum when A is at mean position
D) always remains the same
29. Consider the following statements:
S1: Monkey A will be able to catch the apple.
S2: Path of the apple as observed by monkey A is a straight line.
S3: Tension in the rope when monkey A climbed up the rope with acceleration is more than the weight of monkey A.
The correct statements are:
A) S1 and S2 only B) S2 and S3 only C) S1 and S3 only D) S1, S2 and S3 Passage VII (30 to 32):
Figure shows the two masses M1 and M2 in contact. If a force F is applied on M1.
Then equal acceleration is produced in both the bodies. The expression for acceleration is given by
a =
+
2 1M
M
F
+
=
2 1 2 1M
M
F
M
F
30. Two blocks of masses 4 kg and 6 kg are placed in contact with each other on a frictionless horizontal surface (see above figure). If we apply a push of 5 N on the heavier mass, then force on the lighter mass will be
A) 2 N B) 3 N C) 4 N D) 5 N
31. In the above question, if the force is applied on the lighter mass, then the force exerted by lighter mass on the heavier mass will be
A) 2 N B) 3 N C) 6 N D) 8 N
32. In the above question, the acceleration of the lighter mass will be
A) 0.5 m/s2 B) 1 m/s2 C) (5/6) m/s2 D) (5/4) m/s2
Passage VIII (33 & 34):
In figure two blocks M and m are tied together with an inextensible string. The mass M is placed on a rough horizontal surface with coefficient of friction
µ
and the mass is hanging vertically against a smooth vertical wall.33. Choose the correct statement (s)
A) the system will accelerate for any value of m B) the system will accelerate only when m > M C) the system will accelerate only when m >
µ
M D) nothing can be said34. Choose the correct statement (s) related to the tension T in the string. A) When m <