Test: Motion: 1 - UPSC MCQ

Radius of the orbit (r): 42250 km
Time period (T): 24 hours
Convert Time Period to Seconds:
1 hour = 3600 seconds
24 hours = 24 * 3600 = 86400 second
Circumference of the Circular Orbit:
Formula: Circumference = 2 * π * radius
Substitute radius: Circumference = 2 * π * 42250 km
Value: Circumference ≈ 2 * 3.14159 * 42250 ≈ 265,458 km
Calculate Orbital Speed:
Formula: Speed = Distance / Time
Substitute values: Speed = 265,458 km / 86400 seconds
Value: Speed ≈ 3.07 km/s
The Correct Answer:
The speed of the satellite is approximately 3.07 km/s.
Hence, the correct answer is option B.
Topic in NCERT: MOTION
Line in NCERT: "An artificial satellite is moving in a circular orbit of radius 42250 km. Calculate its speed if it takes 24 hours to revolve around the earth."

To describe the position of an object, a reference point (origin) is necessary. This point serves as a basis for measuring and specifying the location of the object relative to it.

Topic in NCERT: Describing Motion

Line in NCERT: "We describe the location of an object by specifying a reference point."

Radius of truck = r = 140m 
circumfarance
Time taken to cover the distance = t = 5 min 52 sec = 352 sec
Since it complete 2 rounds, therefor distance it travels is 2 times of circumference. 

• The assertion is correct. In uniform motion, the object covers equal distances in equal intervals of time, resulting in a straight line distance-time graph. This reflects a constant speed.
• The reason is also correct. Uniform motion indeed implies a constant speed, which directly corresponds to a straight line on a distance-time graph.
• Therefore, Option A is the correct answer as the reason provides a correct explanation for the assertion.

Topic in NCERT: DISTANCE-TIME GRAPHS

Line in NCERT: "The distance travelled by the object is directly proportional to time taken. Thus, for uniform speed, a graph of distance travelled against time is a straight line."

AS, s=120m (length of train)
t=6 sec (to pass the pole)
v=?
Therefore,
v=s\t
=120\6
=20m\s

As, The train is 120 m long and bridge is 50 m long = {120+ 50 = 170 m }                                                                                   
So, Time taken = distance/speed 
= 170/20
= 8.5 seconds                                                                                           

Speed (1): Calculated using the formula Speed = Distance covered / Time taken.
- Velocity (2): Determined by Velocity = Displacement / Time taken.
- Acceleration (3): Found using Acceleration = Change in velocity / Time taken.
- Average speed (4): Computed as Average speed = Total distance covered / Total time taken.
This differs from instantaneous speed, which is the speed at a specific moment.

An odometer measures the distance travelled by an automobile. It provides the total length of the path covered, irrespective of direction, thus giving the overall distance.

Topic in NCERT: MEASURING THE RATE OF MOTION

Line in NCERT: "Automobiles are fitted with a device that shows the distance travelled. Such a device is known as an odometer."

• Option A: Uniform Motion - Bowling speed in km/h - Incorrect. The term "bowling speed" refers to the speed of a cricket ball, which can vary and is typically non-uniform. Uniform motion means covering equal distances in equal intervals of time, which is not necessarily the case for bowling speed.
• Option B: Non-Uniform Motion - Car moving on a crowded street - Correct. A car moving on a crowded street often has to change its speed frequently due to traffic conditions, which is a perfect example of non-uniform motion.
• Option C: Displacement - Total distance covered - Incorrect. Displacement refers to the shortest distance from the initial to the final position of an object, which is not always equal to the total distance covered.
• Option D: Reference Point - Acceleration - Incorrect. A reference point is a fixed point used to describe the position of an object, while acceleration is the rate of change of velocity.

Topic in NCERT: Non-Uniform Motion

Line in NCERT: "In our day-to-day life, we come across motions where objects cover unequal distances in equal intervals of time, for example, when a car is moving on a crowded street or a person is jogging in a park. These are some instances of non-uniform motion."

To find the velocity with which the ball will strike the ground, we can use the equations of motion under uniform acceleration. The relevant equation here is:

v²=u²+2as

where:

• v is the final velocity
• u is the initial velocity (which is 0 since the ball is gently dropped)
• a is the acceleration due to gravity (10 m/s² in this case)
• s is the distance fallen (20 m)

Substitute the known values into the equation:

v² = 0² + 2 × 10 × 20
v² = 400
v = √400
v = 20 m/s

So, the ball will strike the ground with a velocity of 20 m/s.

Topic in NCERT: Uniformly Accelerated Motion

Line in NCERT: "A ball is gently dropped from a height of 20 m. If its velocity increases uniformly at the rate of 10 m s², with what velocity will it strike the ground?"

Distance: The total distance travelled by the runner is calculated as follows:

• One full lap around the track is the circumference, given by the formula C = 2πr, where r is the radius.
• For a radius of 7 m, the circumference is approximately 43.96 m.
• Since the runner completes 2 laps, the total distance is 2 × 43.96 m = 87.92 m.

Displacement: Displacement is the shortest distance from the initial to the final position:

• After 2 laps, the runner returns to the starting point.
• Thus, the displacement is 0 m.

In summary, the total distance travelled is 87.92 m and the displacement is 0 m.

At maximum height, v = 0 m/s, u = 25 m/s, a = -10 m/s² (upward motion, gravity acts downward).

Use v² = u² + 2as

→ 0 = (25)² + 2(-10)s

→ 0 = 625 - 20s

→ s = 625 / 20 = 31.25 m.

• Statement (i) is correct. The simplest type of motion is indeed motion along a straight line, as mentioned in the provided content.
• Statement (ii) is correct. The magnitude of displacement can be equal to the distance travelled, particularly when the object moves in a straight line without changing direction.
• Statement (iii) is incorrect. The motion of a freely falling body is an example of uniformly accelerated motion, not non-uniformly accelerated motion.
• Statement (iv) is correct. The distance-time graph for uniform motion is a straight line, indicating constant speed over time.
• Therefore, the correct statements are (i), (ii), and (iv).

Circumference = 2πr = 2 × 3.14 × 5 = 31.4 m.

Time for one revolution = 4 s.

Speed = Circumference / Time = 31.4 / 4 = 7.85 m/s.

Uniform circular motion is accelerated because the direction of velocity changes continuously, even if speed is constant.

The slope of a distance-time graph represents the speed  of an object. This is because the slope is calculated as the change in distance divided by the change in time, which is the definition of speed.

Topic in NCERT: DISTANCE-TIME GRAPHS

Line in NCERT: "We can use the distance-time graph to determine the speed of an object."

The slope of the velocity-time graph determines the acceleration.

Topic in NCERT: VELOCITY-TIME GRAPHS

Line in NCERT: "The area under the velocity-time graph gives the distance (magnitude of displacement) moved by the car in a given interval of time."