PHYSICS IIT-JEE Laws of Motion | AskIITian

Class: XI Subject: Physics – Laws of Motion No. of Questions: 30 Duration: 30 Min Maximum Marks: 90

1. A 44 kg child steps onto a scale and the scale reads 430 N. What is the magnitude of the normal force acting on the child? (a) 44 N (b) 215 N (c) 430 N (d) 645 N 2. A 10 kg block is set in motion with an initial speed of 6 m/s on a rough horizontal surface. If the force of friction is 20 N, approximately how far does the block travel before it stops? (a) 1.5 m (b) 3 m (c) 6 m (d) 9 m 3. A 250 N force is directed horizontally as shown to push a 29 kg box up an inclined plane at a constant speed. Determine the magnitude of the normal force FN, and the coefficient of kinetic friction 𝜇𝑘 .

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4. Note the following situations:

In which case will the magnitude of the normal force on the block be equal to 𝑀𝑔 + 𝐹𝑠𝑖𝑛𝜃 ? (a) Case 1 only (b) Case 2 only (c) Both cases 1 and 2 (d) Both cases 2 and 3 5. Two identical blocks are pulled along a rough surface as suggested in the figure. Which one of the following statements is false?

(a) The coefficient of kinetic friction is the same in each case. (b) A force of the same magnitude is needed to keep each block moving. (c) A force of the same magnitude was required to start each block moving. (d) The magnitude of the force of kinetic friction is greater for the block on the right. 6. A crate rests on the flatbed of a truck that is initially travelling at 15 m/s on a level road. The driver applies the brakes and the truck is brought to a halt in a distance of 38 m. If the deceleration of the truck is constant, what is the minimum coefficient of friction between the crate and the truck that is required to keep the crate from sliding? (a) 0.20 (b) 0.30 (c) 0.39 (d) 0.59

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7. A 2 N rock slides on a frictionless inclined plane. Which one of the following statements is true concerning the normal force that the plane exerts on the rock?

(a) The normal force is 0 N (b) The normal force is 2 N (c) The normal force is less than 2 N but more than 0 N (d) The normal force is greater than 2 N 8. In an experiment with a block of wood on an inclined plane, with dimensions as shown in the figure, the following observations are made: (1) If the block is placed on the inclined plane, it remains there at rest. (2) If the block is given a small push, it will accelerate towards the bottom of the incline without any further pushing

Which is the best conclusion that can be drawn from these observations? (a) The coefficient of kinetic friction must be negative. (b) Both coefficients of friction must be less than 0.25 (c) The coefficients of friction must be greater than 0.25 (d) The coefficient of static friction must be less than the coefficient of kinetic friction 9. A rock is suspended from a string, and it moves downward at a constant speed. Which one of the following statements is true concerning the tension in the string if the air resistance is ignored? (a) The tension is zero N (b) The tension is equal to the weight of the rock (c) The tension is less than the weight of the rock. (d) The tension is greater than the weight of the rock.

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10. In a tug – of – war, each man on a 5 man team pulls with an average force of 500 N. What is the tension in the centre of the rope? (a) 0 N (b) 100 N (c) 500 N (d) 2500 N 11. Under what condition(s) will an object be in equilibrium? (a) If the object is either at rest or moving with a constant velocity, it is in equilibrium. (b) If the object is either moving with constant velocity or with constant acceleration, it is in equilibrium. (c) Only if the object is at rest can it be in equilibrium. (d) Only if the object is moving with constant velocity can it be in equilibrium. 12. A 4 – kg block is connected by means of a massless rope to a 2 – kg block as shown in the figure. Complete the following statement: If the 4 kg block is to begin sliding, the coefficient of static friction between the 4 kg block and the surface must be (a) Less than 0. (b) Greater than 2. (c) Greater than 1 but less than 2. (d) Greater than 0.5 but less than 1.

13. A small plane climbs with a constant velocity of 250 m/s at an angle of 280 with respect to the horizontal. Which statement is true concerning the magnitude of the net force on the plane? (a) It is equal to the component of the weight of the plane in the direction of motion (b) It is equal to the weight of the plane. (c) It is equal to the magnitude of the force of air resistance. (d) It is less than the weight of the plane but greater than 0 N.

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14. A muscle builder holds the ends of a massless rope. At the centre of the rope, a 15 kg ball is hung as shown. What is the tension in the rope if the angle 𝜃 in the drawing is 4. 50 ?

(a) 1900 N (b) 940 N (c) 470 N (d) 230 N 15. A block of mass M is hung by ropes as shown. The system is in equilibrium. The point O represents the knot, the junction of the three ropes. Which of the following statements is true with regard to the magnitudes of the three forces in equilibrium?

(a) 𝐹1 = 𝐹2 = 𝐹3 (b) 𝐹1 > 𝐹3 (c) 𝐹2 < 𝐹3 (d) 𝐹1 = 𝐹2 =

𝐹3 2

16. A 20 kg crate is suspended from a fixed beam by two vertical ropes. What is the approximate tension in each rope? (a) 10 N (b) 40 N (c) 100 N (d) 200 N

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17. Two sleds are hooked together in tandem as shown in the figure. The front sled is twice as massive as the rear sled. The sleds are pulled along a frictionless surface by an applied force F. The tension in the rope between the sleds is T. Determine the ratio of the magnitudes of the two forces

𝑇 𝐹

(a) 0.25 (b) 0.33 (c) 0.50 (d) 0.67 18. A woman stands on a bathroom scale in an elevator that is not moving. The scale reads 500 N. The elevator then moves downward at a constant velocity of 5 m/s. What does the scale read when the elevator descends with constant velocity? (a) 100 N (b) 250 N (c) 500 N (d) 600 N 19. A rope connects boats A and B. Boat A starts from rest and accelerates to a speed of 9.5 m/s in a time t = 47 sec. The mass of the boat B is 540 kg. Assuming a constant frictional force of 230 N acting on the boat B, what is the magnitude of the tension in the rope that connects the boats during the time that boat A is accelerating? (a) 340 N (b) 1270 N (c) 230 N (d) 860 N 20. A certain crane can provide a maximum lifting force of 25,000 N. It hoists a 2000 kg load starting at the ground level by applying the maximum force for a 2 second interval; then it applies just sufficient force to keep the load moving upwards at a constant speed. Approximately how long does it take to raise the load from ground level to a height of 30 m? (a) 2 sec (b) 5 sec (c) 8 sec (d) 9 sec

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21. A 10 kg block is pushed against a vertical wall by a horizontal force of 100 N as shown. The coefficient of static friction 𝜇𝑠 between the block and the wall is 0.60 and the coefficient of kinetic friction𝜇𝑘 is 0.40. Which one of the following statements is true if the block is initially at rest?

(a) The total force exerted on the block by the wall is directed horizontally. (b) The block slides down the wall with an acceleration of magnitude 3.8 m/s2. (c) The block will slide down the wall because the force of static friction can no longer be larger than 60N (d) The block will remain at rest because the coefficient of static friction is greater than the coefficient of kinetic friction. 22. A 20 kg package is dropped from a high tower in still air and is tracked by a radar system. When the package is 25 m above the ground, the radar tracking indicates that its acceleration is 7 m/s 2. Determine the force of air resistance on the package. (a) 56 N (b) 28 N (c) 340 N (d) 196 N 23. A 4 kg block and a 2 kg block can move on the horizontal frictionless surface. The blocks are accelerated by a 12 N force that pushes the larger block against the smaller one. Determine the force that the 2 kg block exerts on the 4 kg block.

(a) 4 N (b) 12 N (c) 0 N (d) 8 N

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24. A system of two cables supports a 150-N weight as shown. What is the tension in the right – handcable? (a) 87 N (b) 150 N (c) 170 N (d) 300 N

25. Three spring scales are attached along a straight line as shown. The scale on the left is attached to a wall. A force of 15 N is applied to the scale at the right. What is the reading on the middle scale?

(a) 45 N (b) 10 N (c) 5 N (d) 15 N 26. At a playground, a child slides down a slide that makes an angle of 42°with the horizontal direction. The coefficient of kinetic friction for the child sliding on the slide is 0.2. What is the magnitude of her acceleration during her sliding? (a) 4.7 m/s2 (b) 5.1 m/s2 (c) 5.4 m/s2 (d) 6.3 m/s2

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27. Which statement best explains why the weight of an object of mass m different on Mars than it is on Earth? (a) The mass of Mars is different from that of Earth. (b) The masses and radii of Mars and Earth are not the same. (c) The mass m is further from the Earth’s center when it is on Mars. (d) The mass m will be different on Mars. 28. A 2 kg projectile is fired at an angle of 200. What is the magnitude of the force exerted on the projectile when it is at the highest point in its trajectory? Neglect any effects of air resistance. (a) 19.6 N (b) 14.7 N (c) 9.80 N (d) 4.90 N 29. Two point masses m and M are separated by a distance d. If the separation d remains fixed and the masses are increased to the values 3m and 3M respectively, how doesthe gravitational force between them change? (a) The force will be one – third as great (b) The force will be one – ninth as great (c) The force will be three times as great (d) The force will be nine times as great 30. Two forces act on a 4.5 kg block resting on a frictionless surface as shown. What is the magnitude of the horizontal acceleration of the block?

(a) 1.8 m/s2 (b) 1.2 m/s2 (c) 0.82 m/s2 (d) 3.2 m/s2

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EXPLANATIONS

1.(c) The magnitude of the normal reaction would be equal to the weight of the child which is the reading shown by the scale. 2. (d) The block is going to stop once the force of friction is equal to the retarding force. Hence, using equations of motion, we get: 𝑠=

𝑢2 2𝑎

The retardation would be given by: 𝑎=

20 = 2 𝑚/𝑠 2 10

Hence, we get: 𝑠=

𝑢2 62 = =9𝑚 2𝑎 2 × 2

3.(d) Since we are given that the net speed is equal to zero, so we can say that: 𝐹𝑛𝑒𝑡 = 0Now, along the y – axis, we get: 𝑁 − 𝑚𝑔𝑐𝑜𝑠𝜃 − 𝐹𝑠𝑖𝑛𝜃 = 0And along the x – axis, we get: 𝑚𝑔𝑠𝑖𝑛𝜃 − 𝐹𝑐𝑜𝑠𝜃 + 𝑓𝑘 = 0 Now 𝑓𝑘 = 𝜇𝑘 𝑁 = −𝑚𝑔𝑠𝑖𝑛𝜃 + 𝐹𝑐𝑜𝑠𝜃 = −29 9.8 𝑠𝑖𝑛270 + 250 𝑐𝑜𝑠270 = 94 𝑁 Hence, the normal reaction would be given by: 𝑁 = 𝑚𝑔𝑐𝑜𝑠𝜃 + 𝐹𝑠𝑖𝑛𝜃 = 29 9.8 𝑐𝑜𝑠270 + 250𝑠𝑖𝑛270 = 367 𝑁 And thus, 𝜇 =

𝑓𝑘 𝑁

= 0.26

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4.(a) The normal reaction in each case would be as follows: Case 1: The normal reaction would be given by: 𝑁 = 𝐹𝑠𝑖𝑛𝜃 + 𝑚𝑔 Case 2: The normal reaction would be given by: 𝑁 = 𝐹𝑠𝑖𝑛𝜃 − 𝑚𝑔 Case 3: The normal reaction would be given by: 𝑁 = 𝑚𝑔𝑐𝑜𝑠𝜃 5.(d) The coefficient of kinetic friction doesn’t depend upon the amount of surface in contact. The amount of force of kinetic friction is greater for the block on the right as the length of contact is more.

6. (b) The acceleration produced while covering the distance of 38m would be given by: 𝑎=

𝑢2 152 225 = = 2𝑠 2 × 38 76

Now, if the truck stops, then 225

𝑎 𝜇 = = 76 = 0.30 𝑔 9.8 7.(c) The normal reaction force is equal to 𝑁 = 𝑚𝑔𝑐𝑜𝑠𝜃 = 2𝑐𝑜𝑠𝜃. Hence the normal reaction is less than 2 N.

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8.(c) The Normal reaction of the block would be given by 𝑁 = 𝑚𝑔𝑐𝑜𝑠𝜃 and the force acting along the incline would be given by 𝑚𝑔𝑠𝑖𝑛𝜃. Hence, for the block to be at rest, the friction force should be more than the downward force, i.e. 𝑚𝑔𝑠𝑖𝑛𝜃 ≤ 𝜇𝑚𝑔𝑐𝑜𝑠𝜃. Thus 𝜇 ≥ 𝑡𝑎𝑛𝜃 = 0.25. 9.(b) Since the rock is moving at a constant speed, so the net force acting would be equal to zero. Hence, the tension is equal to the weight of the rock. 10. (a) The tension in the centre of the rope will be equal to 0 N as on each side, the forces have to be equal before any team wines the same. 11. (a) When the object is either at rest of moving with an uniform velocity, then it is in equilibrium. 12. (d) The acceleration of the blocks would be given by: 𝑎=

𝑔 1 − 2𝜇 3

Hence, for the 4 kg block to start sliding, the acceleration should be positive and thus the coefficient of friction must be between 0.5 and 1.

13.(a) The weight of the plane is equal to the component of the force i.e. 𝐹𝑐𝑜𝑠28° = 𝑚𝑔 14.(b) We would have: 2𝑇𝑠𝑖𝑛𝜃 = 𝑚𝑔Hence, 𝑇=

𝑚𝑔 15 × 9.8 = = 936.79 ≈ 940 𝑁 2𝑠𝑖𝑛𝜃 2𝑠𝑖𝑛4.5°

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15. (a) Equating the horizontal forces, give us: 𝐹1 𝑐𝑜𝑠30° = 𝐹2 cos 30° ⟹ 𝐹1 = 𝐹2 And equating the vertical components, give us: 𝐹1 + 𝐹2 sin 30° = 𝐹3 + 𝑀𝑔 ⟹ 2𝐹1

1 = 𝐹1 = 𝐹3 + 𝑀𝑔 2

16.(c) The net tensions would be given by: 2𝑇 = 𝑀𝑔 ⟹ 𝑇 =

𝑀𝑔 20 × 10 = = 100 𝑁 2 2

17.(b) The net force would be equal to: 𝐹 = 3𝑚𝑎 Hence, 𝑇 = 𝑚𝑎 = 𝑚 𝑇

1

𝐹

3

𝐹 3𝑚

𝐹

= . 3

So, = = 0.33.

18.(b) When the elevator is moving downwards with a constant velocity, the net weight is equal to the reading of the scale. 19. (a) The acceleration of the boat A would be equal to: 𝑎=

9.5 47

= 0.2 𝑚/𝑠 2 The net tension would be equal to: 𝑇 = 𝑚𝑎 + 𝑓 = 230 + 540 × 0.2 = 338 𝑁 ≈ 340 𝑁

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20.(c) The net force acting on the load will be given by: 𝐹 = 𝑚𝑔 + 𝑚𝑎 Hence, the acceleration would be given by: 𝑎=

25,000 − 10 = 2.5 𝑚/𝑠 2 2,000

𝐻𝑒𝑛𝑐𝑒the velocity achieved is equal to: 𝑣 = 𝑢 + 𝑎𝑡 = 0 + 2.5 × 2 = 5 𝑚/𝑠 Thus, the time required would be equal to: 𝑡=

𝑠 30 = = 6 𝑠𝑒𝑐 𝑢 5

So, the total time taken would be equal to 8 sec. 21.(c) The maximum frictional force is equal to 60 N which cannot balance the weight of the block which is equal to 100 N.

22.(c) The net force of air resistance would be given by: 𝑓 = 𝑚𝑔 + 𝑚𝑎 = 𝑚 𝑔 + 𝑎 = 20 10 + 7 = 340 𝑁 23.(a) The acceleration of the blocks due to the force would be equal to: 𝑎=

12 4+2

= 2 𝑁Hence, the force exerted by the 2 kg block on the 4 kg block would be equal to 𝑓 =2×2=4𝑁

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24. (d) The forces along horizontal direction would be equal to: 𝑇1 = 𝑇2 cos 30° The forces along vertical direction would be equal to: 𝑇2 sin 30° = 150 25.(b) 2

The reading on the middle scale would be equal to 15 × = 10 𝑁 3

26.(a) The net acceleration of the child would be given by: 𝑎=

1 1 𝑚𝑔 sin 42° − 𝑓 = 𝑚𝑔 sin 42° − 𝜇𝑚𝑔 = 𝑔 sin 42° − 𝜇 = 𝑔 sin 42° − 𝜇 𝑚 𝑚 = 10 0.6691 − 0.2 = 4.69 𝑚/𝑠 2

27.(b) The weight of an object depends on the acceleration due to gravity on the surface of the planet. The acceleration due to gravity on any surface depends on the mass and the radius of that surface. 28.(a) At the highest point of the trajectory, the velocity of the projectile along the vertical direction would be zero. Hence, the net acceleration on the projectile would be equal to 𝑔 = 9.8 𝑚/𝑠 2 Hence, the net force acting on the projectile would be equal to 19.6 N. 29.(d) The gravitational force is directly proportional to the product of the masses of the objects and thus the new force will be nine times as great. 30.

(a)

The net acceleration of the block in the horizontal direction would be 𝑎=

5.9 cos 43° + 3.7 = 1.78 𝑚/𝑠 2 4.5

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