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All questions of September Week 3 for JEE Exam

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The coordinates of centroid of triangle whose vertices are A(-1,-3), B(5,-6) and C(2,3) and origin gets shifted to (1,2) 
  • a)
    (4,-1)
  • b)
    (2,-2)
  • c)
    (0,0)
  • d)
    (-1,4)
Correct answer is option 'D'. Can you explain this answer?

Ishani Menon answered
Finding the Centroid of a Triangle:

The centroid of a triangle is the point where the three medians of the triangle intersect. A median is a line segment that connects a vertex of the triangle to the midpoint of the opposite side. To find the centroid, we need to find the midpoint of each side and then find the intersection point of the three medians.

Finding the Midpoint of a Side:

The midpoint of a line segment is the point that is halfway between the two endpoints. To find the midpoint of a line segment, we use the midpoint formula:

Midpoint = ((x1 + x2) / 2 , (y1 + y2) / 2)

where (x1, y1) and (x2, y2) are the coordinates of the endpoints.

Finding the Coordinates of the Centroid:

Once we have the midpoints of each side, we can find the equation of the three medians and then find their intersection point. The intersection point is the centroid of the triangle.

Let's find the midpoint of each side first:

Midpoint of AB = ((-1 + 5) / 2 , (-3 - 6) / 2) = (2, -4.5)
Midpoint of AC = ((-1 + 2) / 2 , (-3 + 3) / 2) = (0.5, 0)
Midpoint of BC = ((5 + 2) / 2 , (-6 + 3) / 2) = (3.5, -1.5)

Now we can find the equation of the medians. The equation of a line that passes through two points (x1, y1) and (x2, y2) is:

(y - y1) / (y2 - y1) = (x - x1) / (x2 - x1)

Let's find the equation of the median that passes through A:

Midpoint of BC = (3.5, -1.5)
Slope of BC = (-6 - 3) / (5 - 2) = -3
Equation of BC: y + 6 = -3(x - 5) => y = -3x + 21
Slope of median from A to BC = (3 - (-3)) / (2 - 5) = 2/3
Equation of median from A to BC:
y + 3 = (2/3)(x + 1) => y = (2/3)x + (5/3)

Similarly, we can find the equations of the medians that pass through B and C:

Equation of median from B to AC: y + 6 = (1/3)(x - 5) => y = (1/3)x + 11/3
Equation of median from C to AB: y - 3 = (-2/3)(x - 2) => y = (-2/3)x + 5/3

Now we need to find the intersection point of these three medians. We can solve the system of equations:

y = (2/3)x + (5/3)
y = (1/3)x + 11/3
y = (-2/3)x + 5/3

Solving these equations, we get x = -1 and y =

The escape velocity for the moon is nearly
  • a)
    11.2km/s
  • b)
    2.4km/s
  • c)
    24km/s
  • d)
    10km/s
Correct answer is option 'B'. Can you explain this answer?

Rohit Shah answered
About 11.2 km/s
In common usage, the initial point is on the surface of a planet or moon. On the surface of the Earth, the escape velocity is about 11.2 km/s, which is approximately 33 times the speed of sound (Mach 33) and several times the muzzle velocity of a rifle bullet (up to 1.7 km/s).

Gravitational Potential is:
  • a)
    negative, scalar quantity , unit JKg-1
  • b)
    positive, vector quantity , unit JKg-1
  • c)
    positive, scalar quantity , unit JKg-1
  • d)
    negative, vector quantity , unit JKg-1
Correct answer is option 'A'. Can you explain this answer?

Ayush Joshi answered
Gravitational potential (radial fields) at a point in a radial field is the work done per unit mass against the field, in bringing a small mass from infinite distance to the point. Since gravitational fields are attractive and the potential at infinite distance is zero, all points within the field have negative values of potential. Gravitational potential is a scalar quantity with SI unit J kg^-1. The symbol used is mostly V but sometimes or Vr or V(r). A radial gravitational field is one in which the field strength has the same magnitude at all points at a given distance from the center. 

The gravitational potential due to the gravitational force on the earth is defined as the
  • a)
    potential energy multiplied by the mass of the object
  • b)
    potential energy of the mass placed at that point
  • c)
    numerically equal to the potential energy
  • d)
    potential energy of a unit mass at that point.
Correct answer is option 'D'. Can you explain this answer?

Nandini Patel answered
Gravitational Potential
Gravitational Potential is dened as the potential energy of a particle of unit mass at that point due to the gravitational force exerted byearth. Gravitational potential energy of a unit mass is known as gravitational potential.

The point where all the angle bisectors of a triangle meet is
  • a)
    Incenter
  • b)
    Orthocenter
  • c)
    Circumcenter
  • d)
    Excenter
Correct answer is option 'A'. Can you explain this answer?

Om Desai answered
The angle bisectors of the angles of a triangle are concurrent (they intersect in one common point). The point of concurrency of the angle bisectors is called the incenter of the triangle.

When a satellite moves in a circular orbit, the _______acceleration is provided by the gravitational attraction of the earth
  • a)
    tangential
  • b)
    centrifugal
  • c)
    centripetal
  • d)
    fictitious
Correct answer is option 'C'. Can you explain this answer?

Hansa Sharma answered
When any body or particle moves in circular orbit centripetal force acts on it and to move the object centripetal acceleration is necessary. So, when a satellite moves in circular orbit the centripetal acceleration is provided by the gravitational attraction of the earth.

An earth satellite is moved from one stable circular orbit to a farther stable circular orbit. which one of following quantity increases
  • a)
    gravitational potential energy
  • b)
    centripetal acceleration
  • c)
    gravitationl force
  • d)
    linear orbital speed
Correct answer is option 'A'. Can you explain this answer?

Neha Joshi answered
We know that gravitational potential is negative in sign and its magnitude decreases when distance from the massive attracting object increases, hence when considered with sign we can say that gravitational potential increases with increases in distance.

Escape velocity is:
  • a)
    The minimum velocity with which the body has to be projected vertically upwards from the surface of the earth so that it crosses the gravitational field of earth and never returns back on its own.
  • b)
    The minimum velocity with which the body has to be projected vertically upwards from the surface of the earth so that it crosses the gravitational field of earth and returns back
  • c)
    The maximum velocity with which the body has to be projected vertically upwards from the surface of the earth so that it crosses the gravitational field of earth and returns back.
  • d)
    The maximum velocity with which the body has to be projected vertically upwards from the surface of the earth so that it crosses the gravitational field of earth and never returns back on its own
Correct answer is option 'A'. Can you explain this answer?

Geetika Shah answered
Escape velocity is the minimum velocity with which the body has to be projected vertically upwards from the surface of the earth so that it crosses the gravitational field of earth and never returns back on its own.

What could be the maximum value for gravitational potential energy?
  • a)
    1
  • b)
    zero
  • c)
    infinity
  • d)
    1000
Correct answer is option 'B'. Can you explain this answer?

Riya Banerjee answered
As, U=−Gm1m2/r, 
it can be used to describe the potential energy in a system of point charges (or radially symmetric spheres) as a function of their separation distance r, then the maximum value is zero at infinite separation.
Hence, its maximum value is zero at infinity.
 

The energy required to be spent by a satellite of mass m and speed v and orbital radius r in completing a circular orbit once round the earth of mass M is
  • a)
    GMm/r
  • b)
    2GMm/r
  • c)
    GMm/2r
  • d)
    zero
Correct answer is 'D'. Can you explain this answer?

Suresh Iyer answered
As the satellite is bounded by earth's gravitational field and has some velocity, it would completely revolve around the circular orbit without any external energy required.

Velocity of geostationary satellite with respect to earth is
  • a)
    10 ms-1
  • b)
    15 ms-1
  • c)
    zero
  • d)
    1 ms-1
Correct answer is option 'C'. Can you explain this answer?

Neha Joshi answered
Because geostationary satellite ( completes it's rotation in about 24hrs).and it's rotation cycle is same as that of Earth .thus it's velocity is zero with respect to earth

The origin lies on
  • a)
    x – axis only
  • b)
    y – axis only
  • c)
    both axis
  • d)
    none of the axes
Correct answer is option 'C'. Can you explain this answer?

Priya Patel answered
Origin is the only point that lies on both x and y axis, other than that no intersection is possible…
or otherwise for your question,
A point can be represented as (x-coordinate,y-coordinate),so the value in x-coordinate position gives you…the intercept on x-axis and similarly y-coordinate lies on y-axis
so option c is correct

What is gravitational potential?
  • a)
    It is defined as the work done in taking a unit mass from one point to that point
  • b)
    It is defined as the work done in taking a unit mass from infinity to that point
  • c)
    It is defined as the energy spent in taking a unit mass from infinity to that point.
  • d)
    none
Correct answer is option 'B'. Can you explain this answer?

Sanjana Bajaj answered
Understanding Gravitational Potential
Gravitational potential is a fundamental concept in physics, particularly in the study of gravitation and fields. It provides insight into how gravity influences mass in a gravitational field.

Definition of Gravitational Potential
- Gravitational potential at a point in a gravitational field is defined as:
- **The work done in bringing a unit mass from infinity to that point.**
This definition emphasizes that gravitational potential is concerned with the energy required to move an object within a gravitational field.

Why Option B is Correct
- The reason option 'B' is correct can be broken down as follows:
- **Reference Point:** The choice of infinity as a reference point is crucial because at infinity, the gravitational force is effectively zero. This allows us to measure the potential energy relative to a point where gravitational effects can be ignored.
- **Work Done:** The work done against gravitational attraction as an object is brought from infinity to a specified point quantifies the gravitational potential at that point. This work is converted into gravitational potential energy.

Other Options Explained
- **Option A:** Incorrect because it does not specify the reference point (infinity), which is essential for defining gravitational potential.
- **Option C:** While it mentions energy, it inaccurately describes the nature of work done. Gravitational potential is specifically about work done on a unit mass.
- **Option D:** Incorrect as option 'B' is indeed the correct answer.

Conclusion
Understanding gravitational potential is vital for grasping concepts in classical mechanics, as it helps predict the behavior of objects under the influence of gravity.

Earth attracts a body with a force equal to its
  • a)
    weight
  • b)
    area
  • c)
    volume
  • d)
    pollution
Correct answer is option 'A'. Can you explain this answer?

Sharmila Chavan answered
Understanding Gravitational Force
When we talk about the force that Earth exerts on a body, we refer to the gravitational force, which is fundamentally linked to the concept of weight.

What is Weight?
- Weight is defined as the force exerted on an object due to gravity.
- It can be mathematically represented as:
  • Weight (W) = Mass (m) × Gravitational Acceleration (g)


- On Earth, the average gravitational acceleration (g) is approximately 9.81 m/s².

Why is the Correct Answer 'A'?
- The force with which Earth attracts a body is equivalent to its weight. This means that the gravitational pull acting on the body is the same as the weight of that body.
- For example, if an object has a mass of 10 kg, its weight would be:
  • W = 10 kg × 9.81 m/s² = 98.1 N


- This weight represents the gravitational force acting on the object due to Earth's mass.

Other Options Explained
- Area: This does not relate to gravitational force; it measures the extent of a surface.
- Volume: This refers to the space an object occupies, unrelated to gravitational attraction.
- Pollution: This is an environmental issue and has no bearing on gravitational forces.

Conclusion
In conclusion, the Earth attracts a body with a force that is equal to its weight, making option 'A' the correct answer. Understanding this principle is crucial for comprehending fundamental physics concepts related to gravity and motion.

New coordinates of the point (7,-1) would be, if the origin is shifted to the point (1,2) by translation of the axis.
  • a)
    (6,-3)
  • b)
    (-3,6)
  • c)
    (0,0)
  • d)
    (6,3)
Correct answer is option 'A'. Can you explain this answer?

Alok Mehta answered
Let the new origin be (h, k) = (1, 2) and (x, y) = (9, 4) be the given point
Therefore new co-ordinates (X, Y) .
x = X + h and y = Y + k
i.e. 9 = X + 1 and 4 = Y + 2
This gives, X = 8 and Y = 2.
Thus the new co-ordinates are (8, 2)
just a example.

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