When a satellite is on the surface of a planet, it experiences a gravitational force . What is the gravitational force when the satellite is at height , where is the radius of the planet?
1
1.02 W
2
1.00 W
3
0.92 W
4
0.96 W
Official Solution
Correct Option: (4)
The gravitational force at a height from the surface of the planet is given by:
where is the gravitational force at the surface of the planet, and is the radius of the planet. For , we get:
02
PYQ 2016
medium
physicsID: ipu-cet-
Consider a rotating spherical planet. The velocity of a point on its equator is . The effect of rotation of the planet is to make at the equator of at the pole. What is the escape velocity for a polar particle on the planet expressed as a multiple of ?
1
0.5v
2
v
3
4
2v
Official Solution
Correct Option: (4)
The escape velocity is given by:
where is the gravitational acceleration and is the radius. The velocity at the equator is , so the escape velocity is .
03
PYQ 2016
medium
physicsID: ipu-cet-
Kepler's third law states that the square of period of revolution (T) of a planet around the sun, is proportional to third power of average distance, r between the sun and the planet i.e. .
Here, K is constant.
If masses of the sun and the planet are M and m respectively, then as per Newton's law of gravitation, force of attraction between them is , where G is gravitational constant.
The relation between G and K is described as
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2
3
4
Official Solution
Correct Option: (2)
From Kepler's third law and the law of gravitation, using dimensional analysis and considering the constant G, we find that the correct relation is .
04
PYQ 2016
medium
physicsID: ipu-cet-
Use the diagram below to answer the following questions. 40 spheres of equal mass make two rings of 20 spheres each. The ring on the right has a radius twice as large as the ring on the left. If the position of the spheres approximates two uniformly dense rings, which of the following is the concerning a mass placed at position D?
1
The net gravitational force due to the spheres of the larger ring would be zero
2
The net gravitational force due to the spheres of the smaller ring would be zero
3
The net gravitational force due to the spheres of both rings would be zero
4
If the smaller ring were removed, the mass would move towards the centre of the larger ring
Official Solution
Correct Option: (1)
Since the sphere at position D is equidistant from all the spheres in the larger ring, the gravitational forces exerted by all the spheres in the larger ring will cancel out due to symmetry, leading to zero net gravitational force.
05
PYQ 2017
medium
physicsID: ipu-cet-
If the escape speed of a projectile on Earth's surface is and a body is projected out with thrice this speed, then determine the speed of the body far away from the Earth.
1
56.63 km/s
2
33 km/s
3
39 km/s
4
31.7 km/s
Official Solution
Correct Option: (4)
Given:
Escape speed at Earth's surface,
Projection speed,
Step 1: Understand escape speed
The escape speed is the minimum speed needed to break free from Earth's gravitational pull without additional propulsion. At escape speed, the total energy at infinity is zero.
Step 2: Apply energy conservation
At Earth's surface:
Where:
= gravitational constant
= Earth's mass
= Earth's radius
= mass of the projectile
At infinity (far from Earth):
Step 3: Relate to escape speed
We know that escape speed relates to potential energy:
Substituting into the energy equation:
Step 4: Solve for final speed
06
PYQ 2017
medium
physicsID: ipu-cet-
Use the diagram below to answer the following questions. 40 spheres of equal mass make two rings of 20 spheres each. The ring on the right has a radius twice as large as the ring on the left. At what position could a mass be placed so that the gravitational force it would experience would be the same from both rings?
1
A
2
B
3
C
4
D
Official Solution
Correct Option: (2)
The gravitational force on a point due to a ring of mass is given by the formula:
where is the gravitational constant, is the total mass of the ring, is the mass experiencing the force, and is the distance from the center of the ring to the mass. To find the position where the forces from both rings are equal, we equate the gravitational forces from both rings. The forces from the rings at positions A, B, C, and D need to balance. By symmetry and considering the relative distances, position B is the location where the forces from both rings are equal. Thus, the correct answer is (b).
07
PYQ 2017
medium
physicsID: ipu-cet-
A rocket is fired from the Earth towards the Sun. At what distance from the Earth's centre, the gravitational force on the rocket is zero? Mass of the Sun = and mass of the Earth = .
1
2
3
4
Official Solution
Correct Option: (3)
The gravitational force from the Earth and the Sun on the rocket will cancel out at a point where the net gravitational force is zero. The formula for the gravitational force is:
where is the gravitational constant, and are the masses, and is the distance between the objects. For zero gravitational force, the force due to Earth’s gravity and the force due to Sun’s gravity must be equal:
Simplifying the equation:
where is the distance between the Earth and the Sun. Solving for , we find:
Thus, the correct answer is (c).
08
PYQ 2018
medium
physicsID: ipu-cet-
The potential energy of gravitational interaction of a point mass and a thin uniform rod of mass and length , if they are located along a straight line at a distance from each other, is
1
2
3
4
Official Solution
Correct Option: (4)
The potential energy of the gravitational interaction between a point mass and a uniform rod is calculated by integrating the gravitational potential energy contributions from each infinitesimal segment of the rod. The formula for the potential energy is: Hence, the correct answer is (d).
09
PYQ 2018
medium
physicsID: ipu-cet-
Use the diagram below to answer the following questions. 40 spheres of equal mass make two rings of 20 spheres each. The ring on the right has a radius twice as large as the ring on the left.
At what position could a mass be placed so that the net gravitational force that it would experience would be zero?
1
A
2
B
3
C
4
D
Official Solution
Correct Option: (2)
In this problem, we have two rings of mass, one with a radius and the other with a radius . The gravitational forces from the two rings will cancel each other out at a certain point along the line between the two rings.
To find the point where the net force is zero, we use the principle of superposition, where the force due to each ring will act in opposite directions. The gravitational force due to a ring is proportional to the inverse square of the distance.
At point B, the gravitational forces from both rings are equal in magnitude but opposite in direction, thus cancelling each other out, making the net force zero.
