1. What is the formula for instantaneous power if a force \( \mathbf{F} \) acts at an angle θ to velocity \( \mathbf{v} \)?

A. \( P = F v \) B. \( P = F v \sin \theta \) C. \( P = F v \cos \theta \) D. \( P = F / v \)

2. What is the expression for potential energy change related to work done by a conservative force?

A. \( \Delta U = W \) B. \( \Delta U = -W \) C. \( \Delta U = 0 \) D. \( \Delta U = W / 2 \)

3. What is the position of the center of mass for a system of point masses dependent on?

A. The total force B. The vector sum of mass-weighted positions from the origin C. The total energy D. Only the largest mass position

4. When a girl pulls her luggage with force \( \mathbf{F} = 80\,\text{N} \hat{i} - 40\,\text{N} \hat{j} \) through displacement \( \mathbf{x} = 10\,m \hat{i} + 12\,m \hat{j} \), what type of product is used to find the work done?

A. Vector cross product B. Scalar addition C. Vector dot product D. Scalar multiplication only

5. How is force related to change in momentum over time?

A. \( F = \frac{\Delta p}{\Delta t} \) B. \( F = m a \) only C. \( F = p t \) D. \( F = \frac{m}{v} \)

6. What is the definition of linear momentum in physics?

A. The product of mass and acceleration B. The product of mass and velocity C. The ratio of force to time D. The sum of force and velocity

7. What is the formula for work done when force \( F \) acts at an angle \( \theta \) over displacement \( d \)?

A. \( W = F d \sin \theta \) B. \( W = F d \cos \theta \) C. \( W = F d \tan \theta \) D. \( W = F + d \cos \theta \)

8. What effect does friction have on the work done by an external force on a moving system?

A. It increases the total work done B. It does positive work C. It does negative work opposing the motion D. It has no effect on work done

9. The total kinetic energy of a rolling disc is the sum of:

A. Rotational kinetic energy only B. Translational kinetic energy only C. Potential energy and rotational kinetic energy D. Translational and rotational kinetic energies

10. What is the angular acceleration if angular velocity changes from \( 20\pi \) to \( 40\pi \) in 10 seconds?

A. \( 2\pi \, \text{rad/s}^2 \) B. \( 4\pi \, \text{rad/s}^2 \) C. \( 6\pi \, \text{rad/s}^2 \) D. \( \pi \, \text{rad/s}^2 \)

11. A particle has mass 5 units and moves with speed \( v = 3\sqrt{2} \) along the line \( y = x + 4 \). What quantity can be calculated from these data?

A. Angular velocity B. Linear momentum C. Angular momentum D. Power

12. Which equation represents Newton’s second law in terms of momentum?

A. \( F_{\text{net}} = m a \) B. \( F_{\text{net}} = \frac{\Delta p}{\Delta t} \) C. \( p = m v \) D. \( W = \Delta K \)

13. Which of the following best describes power in physical terms?

A. The rate at which kinetic energy decreases B. The force multiplied by the displacement C. The rate at which work is done or energy is transferred D. The product of mass and velocity

14. What is the significance of the vector dot product \( \mathbf{F} \cdot \mathbf{x} \) when calculating work?

A. It calculates scalar magnitude of displacement B. It yields work done by a force along a displacement vector C. It calculates angular displacement D. It is used to find impulse

15. What is the relationship between impulse \( J \) and change in momentum \( \Delta p \)?

A. \( J = m \Delta v \) B. \( J = F \Delta t \) C. \( J = \Delta p \) D. \( J = m a \)

16. Power can also be expressed as:

A. \( P = F v \cos \theta \) B. \( P = F v \sin \theta \) C. \( P = F v \tan \theta \) D. \( P = \frac{F}{v \cos \theta} \)

17. In the problem where an archer fires an arrow, the momentum of the archer after firing is:

A. Equal and opposite to the arrow's momentum B. Zero C. Same direction as arrow's momentum D. Larger than the arrow's momentum

18. In an experiment, if a hockey ball changes velocity direction due to a hit and remains in contact for 5 ms, which physical quantity helps determine the average force exerted by the hit?

A. Velocity B. Total distance C. Impulse and contact time D. Mass only

19. The instantaneous power \( P \) when force \( \mathbf{F} \) acts on a body moving with velocity \( \mathbf{v} \) is:

A. \( P = \mathbf{F} \times \mathbf{v} \) B. \( P = \mathbf{F} + \mathbf{v} \) C. \( P = \mathbf{F} \cdot \mathbf{v} \) D. \( P = \frac{\mathbf{F}}{\mathbf{v}} \)

20. If force \( F \) produces work \( W \) in time \( \Delta t \), power is:

A. \( P = \frac{W}{\Delta t} \) B. \( P = W \times \Delta t \) C. \( P = F \times \Delta t \) D. \( P = \frac{F}{\Delta t} \)

21. What happens to the center of mass position if the masses are relocated closer together but their individual values remain the same?

A. It stays the same B. It shifts towards the largest mass C. It moves to the midpoint of their new locations, weighted by mass D. It moves randomly

22. What happens to momentum when two objects stick together after collision?

A. Total momentum increases B. Total momentum decreases C. Total momentum remains the same D. Total momentum becomes zero

23. If a car of mass \( m_1 \) moving at velocity \( v_1 \) collides with another car of mass \( m_2 \) moving at velocity \( v_2 \), the total momentum is:

A. \( m_1 v_1 - m_2 v_2 \) B. \( m_1 v_1 + m_2 v_2 \) C. \( m_1 + m_2 + v_1 + v_2 \) D. Zero

24. During a collision, the total momentum before and after the event is:

A. Not necessarily equal B. Always conserved (assuming no external force) C. Always zero D. Equal to the total kinetic energy

25. How is impulse related to momentum change?

A. Impulse is the integral of force over displacement B. Impulse equals the change in momentum of the object C. Impulse is the product of mass and velocity D. Impulse equals kinetic energy change

26. The moment of inertia \( I \) of a uniform disc about its axis is:

A. \( \frac{1}{2} m r^2 \) B. \( m r^2 \) C. \( \frac{1}{4} m r^2 \) D. \( 2 m r^2 \)

27. If a force does no work on an object, which condition must be true?

A. The force is zero B. The displacement is zero or force is perpendicular to displacement C. The force and displacement are parallel D. The object moves in the direction of force

28. The number of rotations made by a flywheel during uniform angular acceleration can be found using:

A. \( \theta = \omega_0 t + \frac{1}{2} \alpha t^2 \) B. \( \theta = \omega t \) C. \( \theta = \alpha t \) D. \( \theta = \omega_0 + \alpha t \)

29. What is impulse?

A. Force multiplied by displacement B. Change in kinetic energy C. Product of force and time interval over which it acts D. Velocity change per unit time

30. When a woman carries a load on her head without displacement, what is the work done on the load by her neck/head?

A. Positive B. Negative C. Zero D. Undefined

31. The unit of power is:

A. Joule (J) B. Newton (N) C. Watt (W) D. Pascal (Pa)

32. During an inelastic collision, how does the change in magnitude of momentum compare between two colliding objects?

A. It is larger for the heavier object B. It is larger for the lighter object C. Both experience the same change in magnitude of momentum D. Impossible to determine

33. What is the center of mass for a system of point masses \( m_1, m_2, \dots, m_n \) located at \( x_1, x_2, \dots, x_n \)?

A. \( \frac{m_1 x_1 + m_2 x_2 + \dots + m_n x_n}{n} \) B. \( \frac{m_1 + m_2 + \dots + m_n}{x_1 + x_2 + \dots + x_n} \) C. \( \frac{m_1 x_1 + m_2 x_2 + \dots + m_n x_n}{m_1 + m_2 + \dots + m_n} \) D. \( m_1 x_1 + m_2 x_2 + \dots + m_n x_n \)

34. How do you find the force required to keep a particle in equilibrium when multiple forces act upon it?

A. Sum all forces and apply Newton’s second law B. The force is zero C. Apply the negative of the resultant vector sum of all forces D. Sum the magnitudes of all forces directly

35. The impulse delivered by a bat to a baseball is numerically equal to:

A. Change in velocity of baseball B. Change in momentum of baseball C. Force on the bat D. Momentum of bat

36. What is the SI unit of linear momentum?

A. Newton (N) B. Joule (J) C. kilogram meter per second (kg·m/s) D. Watt (W)

37. What physical quantity do you get by integrating force over a displacement?

A. Power B. Work C. Impulse D. Momentum

38. The magnitude of angular momentum \( L \) of a particle is given by:

A. \( L = m v r \) B. \( L = m v^2 r \) C. \( L = m r^2 \) D. \( L = m \sqrt{v r} \)

39. If the angular velocity of a flywheel doubles under uniform angular acceleration in a given time, how do you find the number of rotations during this interval?

A. Use average angular velocity multiplied by time B. Use initial angular velocity multiplied by time C. Use final angular velocity directly D. Use only moment of inertia

40. If two masses are placed along the x-axis at different points, how do you calculate the center of mass position from the origin?

A. Average of their positions B. Sum of their masses multiplied by their positions divided by total mass C. Difference between their positions D. Sum of distances from the origin

41. If a force does work of 5962.6 J by applying a force at an angle to displacement, what quantity primarily determines the total work done?

A. The force magnitude B. The angle between force and displacement and the distance moved C. The mass of the object D. The friction on the surface

42. According to the work-kinetic energy theorem, work done by a force equals:

A. Change in velocity B. Change in potential energy C. Change in kinetic energy D. Change in momentum

43. Which physical quantity is the scalar product of force and velocity vectors?

A. Work B. Power C. Momentum D. Energy

44. When a baseball is thrown back to the pitcher at a higher speed than its incoming speed, what can be said about the impulse delivered by the bat?

A. It is zero B. It equals the ball’s initial momentum C. It is the change in the ball’s momentum D. It only depends on contact time

45. Which of the following correctly describes the center of mass of a system of point masses?

A. Always at the geometric center B. At the position where the weighted sum of masses balances C. At the location of the heaviest mass D. Always located at the origin

46. If a uniform disc rolls on a horizontal surface without slipping, which energies contribute to the total mechanical energy?

A. Only translational kinetic energy B. Only rotational kinetic energy C. Both translational and rotational kinetic energies D. Potential energy only

47. How is the moment of inertia related to the rotational kinetic energy of a rolling disc?

A. Energy is independent of the moment of inertia B. Rotational kinetic energy is half the moment of inertia times angular velocity squared C. Rotational kinetic energy equals moment of inertia times angular velocity D. Rotational energy is proportional to mass only

48. What is the mathematical expression for the work done by a constant force acting at an angle θ to the direction of displacement?

A. \(W = F \cdot x\) B. \(W = F x \sin \theta\) C. \(W = F x \cos \theta\) D. \(W = F / x\)

49. What happens to an archer’s velocity when firing an arrow on frictionless ice?

A. Archer stays at rest B. Archer moves in the same direction as the arrow C. Archer moves opposite to the firing direction due to conservation of momentum D. Archer moves randomly

50. Power is defined as:

A. The amount of work done per unit distance B. The rate at which work is done C. The product of force and velocity D. The total energy of a system