# Engineering Physics Questions and Answers – Motion in a Plane – 2

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This set of Engineering Physics Questions and Answers for Experienced people focuses on “Motion in a Plane – 2”.

1. The total path length is always equal to the magnitude of the displacement vector of a particle.
a) True
b) False

Explanation: The displacement depends only on the end points while the path length depends on the actual path. The two quantities are equal only if the direction of motion of the object does not change. In all other cases, the path length is greater than the magnitude of displacement.

2. A passenger arriving in a new town wishes to go from the station to a hotel located 10km away on a straight road from the station. A dishonest cabman takes him along a circuitous path 23km long and reaches the hotel in 28 minutes, what is the average speed of the taxi?
a) 21.43km/h
b) 75km/h
c) 49.3km/h
d) 21km/h

Explanation: Magnitude of displacement = 10km
Total path length = 23km
Time taken = 28mins = 28/60h = 7/15h
Average speed = (Total path lenght)/(Time taken) = 23/(7/15) = 49.3km/h.

3. The net acceleration of a particle in circular motion is ___________
a) Towards the centre
c) Irregular
d) Circular in motion

Explanation: The net acceleration of a particle in a circular motion is towards the centre only if its speed is constant.
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4. A scalar quantity is conserved in a process.
a) True
b) False

Explanation: Scalar quantities like kinetic energy are not conserved in an inelastic collision. Moreover, vector quantities like linear momentum are conserved.

5. A projectile fired from the ground follows a parabolic path. At what position will the speed of projectile be minimum?
a) At the top of the path
b) At the beginning of the path
c) While travelling along the path
d) Never

Explanation: The speed of the projectile will be minimum at the top of the path. This is because a horizontal component of velocity will remain constant throughout the motion whereas the vertical component of the velocity is zero at the top.

6. Two bullets are fired simultaneously, horizontally and with different speeds from the same place. Which bullet will hit the ground first?
a) The faster one
b) Depends on their mass
c) The slower one
d) Both will reach simultaneously

Explanation: Both the bullets will reach simultaneously because
T = √(2h/g) Time t does not depend on horizontal speed.

7. Three particles A,B and C are projected from the same point with the same initial speed making angles 30°,45° and 60° respectively with the horizontal. Which of the following statements is correct?
a) A, B and C have unequal ranges
b) Ranges of A and C are equal and less than that of B
c) Ranges of A and C are equal and greater than that of B
d) A, B and C have equal ranges

Explanation: RA = (u2 sin60°)/g = √3/2 u2/g
RB = (u2 sin90°)/g = u2/g
Rc = (u2 sin120°)/g = √3/2 u2/g
Ranges A and C are equal but less than that of B.

8. A body executing uniform circular motion has at any instant is velocity vector and acceleration vector ___________
a) Along the same direction
b) In opposite direction
c) Normal to each other
d) Not related to each other

Explanation: Velocity is along the tangent to the circular path and acceleration vector is along the radius. Thus a body executing uniform circular motion at any instant has velocity vector and acceleration vector normal to each other.

9. Two vectors have a resultant equal to either. The angle between them is ___________
a) 60°
b) 120°
c) 90°
d) 100°

Explanation: R = √(P2+Q2+2PQcosθ)
p2 = 2p2 (1+cosθ)
1+cosθ = 1/2
Cosθ = -1/2 = cos 120°
θ = 120°.

10. A body A is dropped from vertically from the top of a tower. If another identical body is thrown horizontally from the same point at the same instant, then ___________
a) A will reach the ground earlier
b) B will reach the ground earlier than A
c) Both A and B will reach the ground simultaneously
d) Depends on external factors

Explanation: Both A and B will reach the ground simultaneously. Both have zero initial velocity and cover the same height under the acceleration due to gravity.

11. Which of the following is constant in projectile motion?
a) Horizontal component
b) Vertical component
c) Velocity of projection
d) Acceleration of projected object

Explanation: The horizontal component is constant in a projectile motion. It is not affected by the force of gravity.

12. At the highest point of a projectile, its velocity and acceleration are at an angle of ___________
a) 0°
b) 45°
c) 90°
d) 180°

Explanation: At the highest point of projectile, it has only horizontal velocity while the acceleration due to gravity acts vertically downwards. Therefore they are at an angle of 90°.

13. An aeroplane flying horizontally with a speed of 360km/h releases a bomb at a height of 490m from the ground. If g=9.8m/s2, it will strike the ground at ___________
a) 10km
b) 100km
c) 1km
d) 16km

Explanation: Time is taken by the bomb to fall through a height of 490m,
t = √(2h/g) = √((2×490)/9.8)=10s
Distance at which the bomb strikes the ground = Horizontal velocity × time = 1km.

14. A stone tied to the end of string 80cm long is whirled in horizontal circle with a constant speed. If the stone makes 14 revolutions in 25 sec, what is the magnitude of acceleration of the stone?
a) 680 cm/s2
b) 860 cm/s2
c) 720 cm/s2
d) 990 cm/s2

Explanation: a = rω2 = r(2πn/t)2
a = (80×4×(22/7)2×142)/142 = 990cm/s2.

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