B.Sc. PHYSICS (FYUGP) FIRST SEMESTER | FUNDAMENTALS OF PHYSICS | ASSIGNMENT 2 | Answers

Questions

1. A certain force gives a 2 kg object an acceleration of 0.5 m/s2. Find the acceleration produced by 

the same force on a 10 kg object. 

2. A force of 12 N gives an object an acceleration of 4 m/s2. Calculate the force required to give it an 

acceleration of 10 m/s2. 

3. A body of mass 2 kg is acted upon by two mutually perpendicular forces 2 N and 4 N. Find the 

acceleration produced on the body. 

4. While driving a car with a speed of 72 km/h, the driver saw a child in the middle of the road. If he 

took 4 seconds to stop the car just in front of the child, what is the retarding force applied by the 

break? 

5. The force exerted on a particle of mass 5 kg is given by 𝐹

 rest, find its position at after 3 seconds. 

⃗  = (5𝑖̂ + 15𝑗̂) N. If the particle starts from 

6. A force produces an acceleration a1 on a body of mass m1 and a2 on a body of mass m2. Find the 

acceleration produced by the same force on the combined mass (m1+m2). 

7. A 7 kg object is subjected to two forces F⃗ 1 = (20𝑖̂ + 30𝑗̂) N and  F⃗ 2 = (8𝑖̂ -5𝑗̂) N. Find the 

magnitude of the resulting acceleration. 

8. An object of mass 0.1 kg at rest is acted upon by a force (0.1𝑖̂ – 0.4𝑗̂) N, for a period of 2 s. What 

is the velocity acquired by the object in the direction of the force? 

9. Two forces of equal magnitude have their resultant equal to either force in magnitude. What is the 

angle between the two forces? 

10.  A force is inclined at 50o to the horizontal. If its horizontal component is 50 N, find its magnitude 

and the vertical component. 

11. A child pulls a rope attached to a stone with a force of 60 N. The rope makes an angle of 40o to the 

ground. (i) Calculate the effective value of the pull tending to move the stone along the ground. (ii) 

Calculate the force tending to lift the stone. 

12. Forces of 5√2N and 6√2N are acting on a body of mass 1000 kg at an angle 60o with each other. 

Find the acceleration, distance covered and the velocity of the mass after 5 seconds. 

13. The distance travelled by a body is directly proportional to the time. Is there any external force 

acting on it? Justify your answer. 

14. A constant retarding force of 50 N is applied to a body of mass 20 kg moving initially with a speed 

of 15 m/s. How long does the body takes to stop?  

15. A body of mass 5 kg is acted upon by two perpendicular forces of magnitude 8 N and 6 N. Find the 

magnitude and direction of the acceleration of the body. 

16. Why is it easier to pull a lawn mower than to push it?

Answers

Here are the very short, precise answers:

1. 0.1 m/s²

2. 30 N

3. √5 ≈ 2.24 m/s²

4. –1000 N(wrong)

5. (3.0 m , 9.0 m)

6. (m₁a₁m₂a₂)/(m₁a₂+m₂a₁)

7. ≈5.44 m/s²

8. (0.2 m/s , –0.8 m/s)

9. 120°

10. Magnitude = ≈65 N, Vertical = ≈50 N

11. (i) ≈46 N, (ii) ≈39 N

12. a ≈0.014 m/s², s ≈0.175 m, v ≈0.07 m/s

13. No — motion is uniform.

14. 6 s

15. Magnitude = 2 m/s², Direction = 36.9°

16. Pull reduces normal reaction (less friction).

Would you like them also in formula form or explained briefly?

 — here are only the formulas & calculation steps (no explanations):

---

1.
$F = ma \Rightarrow F = 2 \times 0.5 =1 \, \text{N}$
$a = \dfrac{F}{m} = \dfrac{1}{10} =0.1 \, \text{m/s}^2$

---

2.
$F = ma =12 \Rightarrow m = \dfrac{12}{4}=3 \, \text{kg}$
$F' = ma' = 3 \times 10 =30 \, \text{N}$

---

3.
$F = \sqrt{2^2+4^2}= \sqrt{20}=4.47\, \text{N}$
$a= \dfrac{F}{m}=\dfrac{4.47}{2}=2.24 \, \text{m/s}^2$

---

4.(wrong)
$u=20\, \text{m/s}, v=0, t=4 \Rightarrow a =\dfrac{v-u}{t}=-5\, \text{m/s}^2$
$F = ma =20 \times (-5) = -100\,\text{N}$

---

5.
$a = \dfrac{\vec{F}}{m}=(1,3)\,\text{m/s}^2$
$\vec{r} =\dfrac{1}{2}\vec{a}t^2 =\dfrac{1}{2}(1,3)(3^2)=(4.5,13.5)\,\text{m}$

---

6.
$F = m_1 a_1 = m_2 a_2\Rightarrow a= \dfrac{F}{m_1+m_2}=\dfrac{m_1 a_1}{m_1+m_2} =\dfrac{m_2 a_2}{m_1+m_2}$

---

7.
$\vec{F}=(28,25)\Rightarrow |\vec{F}|=\sqrt{28^2+25^2}=37.34$
$a=\dfrac{37.34}{7}=5.33$

---

8.
$a=\dfrac{F}{m}=(1,-4)$
$v=\vec{a}t=(1,-4)\times2=(2,-8)$

---

9.
$R=F \Rightarrow 2F\cos\dfrac{\theta}{2}=F \Rightarrow \theta=120^\circ$

---

10.
$F\cos50^\circ=50\Rightarrow F=\dfrac{50}{\cos50^\circ}=64.99$
$F_v=F\sin50^\circ= \approx49.8$

---

11.
(i)$F_x=60\cos40^\circ=45.96$
(ii)$F_y=60\sin40^\circ=38.57$

---

12.
Resultant force:
$F=\sqrt{(5\sqrt2)^2+(6\sqrt2)^2+2(5\sqrt2)(6\sqrt2)\cos60^\circ}=20\,\text{N}$
$a=\dfrac{20}{1000}=0.02$
$v=at=0.1$
$s=\dfrac{1}{2}at^2=0.25$

---

13.
$s\propto t \Rightarrow v=\text{constant}, a=0, F=0$

---

14.
$a = \dfrac{F}{m}=\dfrac{-50}{20}=-2.5$
$t=\dfrac{v}{|a|}=\dfrac{15}{2.5}=6 \,\text{s}$

---

15.
$F=\sqrt{8^2+6^2}=10 \Rightarrow a=\dfrac{10}{5}=2$
$\theta=\tan^{-1}\left(\dfrac{6}{8}\right)=36.9^\circ$

---

16.
Pull: $F\sin \theta \uparrow \Rightarrow N\downarrow \Rightarrow f=\mu N\downarrow$

---

Need anything else? Comment

Assignment 1 Answers

Here are the answers along with their questions:

---

1. What did Galileo discover in his legendary experiment on the Leaning Tower of Pisa?
👉 Galileo discovered that objects of different masses fall at the same rate when air resistance is negligible.

---

2. Before the time of Galileo and Newton, some learned scholars thought that a stone dropped from the top of a tall mast of a moving ship would fall vertically and hit the deck behind the mast by a distance equal to how far the ship had moved forward while the stone was falling. In light of your understanding of Newton’s first law, what do you think about this?
👉 According to Newton’s first law, the stone keeps the forward motion of the ship. So, it falls directly at the base of the mast, not behind it.

---

3. Consider a ball at rest in the middle of a toy wagon. When the wagon is pulled forward, the ball rolls against the back of the wagon. Discuss and interpret this observation in terms of Newton’s first law.
👉 The ball tends to stay at rest (inertia) while the wagon moves forward. Hence, the wagon moves ahead from under the ball, making it roll to the back.

---

4. A space probe may be carried by a rocket into outer space. What keeps the probe moving after the rocket no longer pushes it?
👉 The probe continues moving due to inertia (Newton’s first law). No force is needed to keep it moving in space once it has been set in motion.

---

5. A child learns in school that Earth is travelling faster than 100,000 kilometers per hour around the Sun and, in a frightened tone, asks why we aren’t swept off. What is your explanation?
👉 We, the air, and everything on Earth move with the Earth. There is no relative motion, so we don’t get swept off.

---

6. If you toss a coin straight upward while riding in a train, where does the coin land (i) when the motion of the train is uniform along a straight-line track? (ii) When the train slows while the coin is in the air?
👉 (i) The coin lands back in your hand since it shares the train’s motion.
👉 (ii) The coin lands ahead of you because the train slows down while the coin keeps moving forward.

---

7. A ball is thrown straight upward and leaves your hand at 20 m/s. What predictions can you make about the ball?
👉 It will rise until its velocity becomes zero, then fall back with equal speed in the opposite direction. Total time in air ≈ 4.08 s, maximum height ≈ 20.4 m.

---

8. What is the gain in speed per second for a freely falling object? When an object is thrown upward, how much speed does it lose each second (ignoring air resistance)?
👉 A freely falling object gains 9.8 m/s each second. When thrown upward, it loses 9.8 m/s each second.

---

9. Suppose that a freely falling object were somehow equipped with a speedometer. By how much would its reading in speed increase with each second of fall? Suppose that the freely falling object were also equipped with an odometer. Would the readings of distance fallen each second indicate equal or different falling distances for successive seconds?
👉 Speed increases by 9.8 m/s each second. The distances are unequal—greater with each successive second (1st second = 4.9 m, 2nd second = 14.7 m, etc.).

---

10. What is the distance fallen for a freely falling object 1 s after being dropped from a rest position? What is the distance for a 4-s drop?
👉 After 1 s: 4.9 m.
👉 After 4 s: 78.4 m.

---

11. You toss a ball straight up with an initial speed of 30 m/s. How high does it go, and how long is it in the air (ignoring air resistance)?
👉 Maximum height = 45.9 m.
👉 Total time in air ≈ 6.12 s.

---

12. A ball is tossed with enough speed straight up so that it is in the air several seconds.
(a) At the top, velocity = 0.
(b) 1 s before top, velocity = +9.8 m/s upward.
(c) Change in velocity = –9.8 m/s.
(d) 1 s after top, velocity = –9.8 m/s downward.
(e) Change in velocity = –9.8 m/s.
(f) In 2-s interval, total change = –19.6 m/s.
(g) Acceleration = –9.8 m/s² at all times, even when velocity = 0.

---

13. Rakesh stands at the edge of a cliff and throws a ball nearly straight up at a certain speed and another ball nearly straight down with the same initial speed. If air resistance is negligible, which ball will have the greater speed when it strikes the ground below?
👉 Both will have the same speed when they reach the ground.

---

14. When a ball is tossed straight up, it momentarily comes to a stop at the top of its path. Is it in equilibrium during this brief moment? Why or why not?
👉 No, it’s not in equilibrium because gravity still acts on it, giving it acceleration downward.

---

15. Consider a pair of forces, one having a magnitude of 20 N and the other a magnitude of 12 N. What is the strongest possible net force for these two forces? What is the weakest possible net force?
👉 Strongest = 32 N (when same direction).
👉 Weakest = 8 N (when opposite direction).

---

16. If there were no air resistance, why would it be dangerous to go outdoors on rainy days?
👉 Raindrops would fall with very high speed (due to gravity only) and could cause injury.

---

17. Why does a stream of water get narrower as it falls from a faucet?
👉 As water falls, its speed increases due to gravity. The same volume flows each second, so the stream narrows.

---

18. Correct your friend who says, “The car rounded the curve at a constant velocity of 100 km/h.”
👉 The car has constant speed, not constant velocity, because velocity includes direction, and direction changes in a curve.

---

19. Cite an instance in which your speed could be zero while your acceleration is nonzero.
👉 At the highest point of a vertical throw, speed = 0, but acceleration = –9.8 m/s².

---

20. (a) Can an object be moving when its acceleration is zero? If so, give an example. (b) Can an object be accelerating when its speed is zero? If so, give an example.
👉 (a) Yes, a car moving at constant speed on a straight road.
👉 (b) Yes, at the top of a vertical throw.

---

21. A friend says that if a car is travelling toward the east, it cannot at the same time accelerate toward the west. What is your response?
👉 It can—when the car is slowing down while moving east, its acceleration is toward the west.

---

22. Can an automobile with a velocity toward the north simultaneously have an acceleration toward the south? Convince your classmates of your answer.
👉 Yes, if the automobile is slowing down while moving north, the acceleration is southward.

---

23. Can you cite an example in which the acceleration of a body is opposite in direction to its velocity?
👉 A ball thrown upward: velocity is upward, but acceleration is downward.

---

24. Can an object reverse its direction of travel while maintaining a constant acceleration? If so, cite an example.
👉 Yes, a ball thrown upward reverses direction at the top while acceleration (gravity) remains constant downward.

---

25. If you drop an object, its acceleration toward the ground is 9.8 m/s². If you throw it down instead, would its acceleration after throwing be greater than 9.8 m/s²? Why or why not?
👉 No, the acceleration is still 9.8 m/s². The initial velocity is greater, but gravity gives the same acceleration.

---