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.

Forces are said to be balanced when two equal and opposite forces acts on an object which makes net force to be zero. Balanced forces are acting means object will be rest. When unbalanced forces are acting on object it starts moving in the direction of force. Example a book kept on table has two forces gravitational force acting downwards and normal force acting upwards. As two forces are equal and opposite the net force will be zero and object remains at rest. and if resultant force is zero the object would be moving with uniform acceleration as there would be no acceleration

So option D is correct

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.

AS, d=120m (length of train)
t=6 sec (to pass the pole)
v=?
Therefore,
v=d\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 = DISTANCE / TIME 
DISTANCE = 100M 
TIME = 50 SEC 
THEN, SPEED =100M / 50 SEC 
SPEED = 2 M / S

A curved line in a speed - time graph means non - uniform motion. In speed - time graph, uniform motion is represented by straight line parallel to time zone . We know that, slope of the velocity - time graph gives the acceleration of the body. If the velocity Time graph is a curved line, this means it's slope changes at every instant. Thus the body is said to be in non - uniform motion. 

So option A is correct

The correct option is B.
For a body moving at a uniform velocity you can calculate the speed by dividing the distance traveled by the amount of time it took, for example one mile in 1/2 hour would give you 2 miles per hour.
In order to find the velocity of the moving object, you will need to divide the change in position by the change in time. Specify the direction moved, and you have the average velocity.
Calculating acceleration involves dividing velocity by time — or in terms of SI units, dividing the meter per second [m/s] by the second [s]. Dividing distance by time twice is the same as dividing distance by the square of time. Thus the SI unit of acceleration is the meter per second squared 
Average speed is calculated by dividing distance by time (e.g. miles/hour). Okay we're going to talk about average speed, instantaneous speed is the distance that you're covering at a specific time. So 100 kilometers an hour, average speed is the total distance you're going to cover over a period of time.

• 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.

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:

The area under the velocity-time graph represents the displacement of an object. The displacement is calculated by finding the area under the curve of the graph. If the graph is irregular, it can be divided into simpler geometric shapes (like rectangles, triangles, and trapezoids) and their areas can be summed. For more complex shapes, integration can be used to find the exact area under the curve, which corresponds to the displacement. The slope of the velocity-time graph, on the other hand, gives the acceleration.

• 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).

first equation of motion is : v = u + at

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.

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

The acceleration mentioned is due to the force of gravity. This is a force of attraction based on the mass of an object and the distance between the two objects Newton's law of universal gravitation. Generally on the surface of the earth we treat this as 9.8 m/sec^2 or 32 ft/sec^2. The way that Einstein describes it is that mass curves spacetime, thus space itself is pushing down on the falling object and is the cause of the force. 

So option C is correct.