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All questions of Acceleration for Grade 9 Exam

If the signs of the velocity and acceleration of a particle are the same, the speed of the particle ______________.
  • a)
    Remains same
  • b)
    Increases
  • c)
    Decreases
  • d)
    Cannot conclude anything
Correct answer is option 'B'. Can you explain this answer?

Pooja Shah answered
In this question, it has been asked about the signs of velocity and acceleration not about the values of velocity and acceleration.
So, if both the entities have same the signs, then the speed of the object will increase.
If it is accelerating in the positive direction, the negative velocity is decreasing, and the object is slowing down.

A boy throws up a ball in a stationary lift and the ball returns to his hands in 10 s. Now if the lift starts moving up at a speed of 5 m/s. The time taken for a ball thrown straight up to return to his hands is:
  • a)
    more than 10 s
  • b)
    Less than 10 s
  • c)
    insufficient information given
  • d)
    equal to 10 s
Correct answer is option 'D'. Can you explain this answer?

Suresh Iyer answered
 Lift moving with Uniform speed  = 5m / s
Ball is thrown inside the lift
The uniform velocity of the lift does not affect the relative velocity of the ball with respect to the boy.
Relative velocity of ball = 49m/s
⇒ Relative acceleration = 9.8
Thus, u(relative) = velocity of bell
t = 2u/ gr
​= (2 × 49) / 9.8
⇒ t = 10s
so, the ball will still return in 10 secs

The dimensions of instantaneous acceleration is:
  • a)
    [ LT-2]
  • b)
    [L/T2]
  • c)
    [L/T-1]
  • d)
    [LT-1]
Correct answer is option 'A'. Can you explain this answer?

Neha Joshi answered
Instantaneous acceleration is rate of change of instantaneous velocity with time or velocity upon total time, hence we get its dimension is same as of acceleration i.e. LT-2

 What does this graph indicate about the motion of an object?
  • a)
    Object is moving in positive direction with positive acceleration
  • b)
    Object is moving in negative direction with negative acceleration
  • c)
    An object is moving in positive direction till time t1, and then turns back with the same Velocity
  • d)
    Object is moving in positive direction with negative acceleration
Correct answer is option 'D'. Can you explain this answer?

Top Rankers answered
Through the given graph we get that:
Velocity is decreasing from a positive constant to some negative number with zero at t1
Distance from the original point increases from zero to t1 and then it decreases afterwards.
The object is moving in a positive direction at first and after time t1 it moves in a negative direction.

The position x of a particle varies with time (t) as x = 3t2 – 2t3  .The acceleration of the particle will be zero at time
  • a)
    1
  • b)
    3/2
  • c)
    0
  • d)
    1/2
Correct answer is option 'D'. Can you explain this answer?

Lavanya Menon answered
We know that acceleration is the second derivative of change in displacement wrt time, hence we get a = 6 - 12t
When a = 0 = 6 -12t ;
We get t = ½ 

The displacement of a particle along x-axis is given by x = 4 + 6t + 5t2. Its acceleration at t = 2s
  • a)
    2 m/s2
  • b)
    10 m/s2
  • c)
    1000 m/s2
  • d)
    100 m/s2
Correct answer is option 'B'. Can you explain this answer?

Mira Sharma answered
usingdifferentiation

x = 18t + 5t^2

dx/dt = 18 + 10t

v = 18 + 10t

at t = 2s

v = 18 + 10x2

= 18 + 20 =38m/s

at t = 3s

v = 18 + 10x3

= 18 + 20 = 48m/s

vav= 38+48/2= 43m/s

dv/dt = 10

a = 10

a =10m/s^2

On acceleration-time graph the area under the curve equals the:
  • a)
    Meaningless
  • b)
    Change in velocity
  • c)
    Displacement
  • d)
    Change in acceleration
Correct answer is option 'B'. Can you explain this answer?

Nandini Patel answered
The area under an acceleration graph represents the change in velocity. In other words, the area under the acceleration graph for a certain time interval is equal to the change in velocity during that time interval.

The value of acceleration due to gravity on earth is.
  • a)
    9.8ms−2.
  • b)
    15376
  • c)
    227004
  • d)
    127008
Correct answer is option 'A'. Can you explain this answer?

Ishan Ghosh answered
Understanding Acceleration Due to Gravity
The acceleration due to gravity (g) is a fundamental constant that defines the acceleration experienced by an object when it is in free fall near the Earth's surface.
Value of g
- The standard value of acceleration due to gravity on Earth is approximately 9.8 m/s².
- This means that, neglecting air resistance, an object will increase its velocity by 9.8 meters per second for every second it is falling.
Why g is Approximately 9.8 m/s²
- Earth's Mass and Radius: The value of g is influenced by the mass of the Earth and its radius. The more massive the Earth, the stronger the gravitational pull. Similarly, the closer you are to the Earth's center (i.e., the smaller the radius), the stronger the gravitational force.
- Universal Law of Gravitation: According to this law, every mass attracts every other mass. The force of gravity is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Variations of g
- It's important to note that the value of g can vary slightly depending on where you are on Earth, due to factors such as altitude and the Earth's rotation. For instance, g is slightly less at the equator compared to the poles.
Conclusion
- Among the options provided, 9.8 m/s² is the only correct and scientifically accepted value for the acceleration due to gravity on Earth, making option 'A' the right choice. Other values like 15376, 227004, and 127008 are incorrect and do not represent the gravitational acceleration experienced on our planet.

The earth's gravitational force at someplace in space causes an acceleration of 7m/s2 in a 1kg mass.What will be the acceleration of a 5kg mass at the same place?
  • a)
    7m/s2
  • b)
    35m/s2
  • c)
    1.4m/s2
  • d)
    3.5m/s2
Correct answer is option 'A'. Can you explain this answer?

Hansa Sharma answered
The acceleration due to gravity does not vary with the change in the mass of the object as it is a dimensionless quantity representing the amount of matter in a particle or object.
Therefore, the acceleration of a 5 kg mass at the same place is 7m/s2.

The diameters of two planets are in the ratio 4:1 and their mean densities in the ratio 1:2. The acceleration due to gravity on the planets will be in ratio
  • a)
    2:1 
  • b)
    2:3
  • c)
    1:2
  • d)
    4:1
Correct answer is option 'A'. Can you explain this answer?

Gaurav Kumar answered
Acceleration due to gravity is given by the equation g = GM/R2 (at surface)
so g1 = GM1 /R12 and g2 = GM2 /R22 (gravities at planets 1 and 2)
also M1/M2 = V1p1/V2p2 = R13 p1/ R23 p2 (as V = 4/3 π r3
Therefore, g1/g2 = R1 ρ1 / R2 ρ2 = (4/1) x (1/2) = 2:1

Radius of planet A is twice that of planet B and the dencity of A is one third that of B . The ratio of the acceleration due to gravity at the surface of A to that at the surface of B is.-
  • a)
    2:3
  • b)
    3:2
  • c)
    3:4
  • d)
    4:3
Correct answer is option 'A'. Can you explain this answer?

Naina Sharma answered
Radius of planet A is twice that of planet B and the density of A is one-third that of B.
so, the radius is
The density is
We know that,
The acceleration due to gravity
The ratio of the acceleration due to gravity at the surface of A to that at the surface of B is
We know,
Mass = density X Volume
Hence, the ratio of the acceleration due to gravity is 2:3.

Force of gravity is least at
  • a)
    The equator
  • b)
    The poles
  • c)
    A point in between equator and any pole
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Bhargavi Bajaj answered
Explanation:
Gravity is the force that attracts two bodies towards each other. The force of gravity depends on the mass of the two bodies and the distance between them. The closer the two bodies are, the stronger the force of gravity between them.

Gravity at Equator, Poles and in between:
- The Earth is not a perfect sphere, it is slightly flattened at the poles and bulging at the equator due to its rotation. This means that the distance from the center of the Earth to a point on the equator is greater than the distance from the center of the Earth to a point on the poles.
- As the force of gravity depends on the distance between two bodies, it is least at the equator where the distance from the center of the Earth is the greatest.
- At the poles, the force of gravity is the greatest as the distance from the center of the Earth is the least.
- The force of gravity at a point in between the equator and any pole would be somewhere in between the force of gravity at the equator and the force of gravity at the poles.

Conclusion:
Therefore, the correct answer is option 'A' as the force of gravity is the least at the equator due to the greater distance from the center of the Earth.

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