Tricky questions

## Gravitation

- Stand out of the queue by practicing questions that most of the students get wrong
1
Discuss about net force acting on one mass by number of bodies: superposition principle.
When no. of bodies are present in a system, the net gravitational force acting on a body is the resultant of the gravitational pull of all the bodies. And there directions are along the line joining the center of mass of any two bodies. Most of the time, students forget to consider the direction of gravitational pull.
Two stationary particles of masses and are at distance d apart. A third particle, lying on the line joining the particles, experiences no resultant gravitational force. The distance of this particle from is
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Four similar particles of mass m are orbiting in a circle of radius r in the same angular direction because of their mutual gravitational attractive force. Velocity of a particle is given by.
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Four particles having masses m,2 m, 3 m and 4 m are placed at the four corners of a square of edge a.Find the gravitational force acting on a particle of mass m placed at the center.
2
Concept of negative mass to find gravitational field.
Sometime spherical cavity are present in the stationary bodies due to which gravitational pull are effected. Negative mass concept is introduced to solve this type of problem.
A solid sphere of uniform density and radius R applies a gravitational force of attraction equal to  on a particle placed at A, distant from the center of the sphere. A spherical cavity of radius is now made on the sphere with cavity now applies a gravitational force. Then  will be
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3
Finding variation of acceleration due to gravity with latitudinal position on earth.
Most of the students get confused while solving the problem having variation of acceleration due to gravity. It is observed that acceleration due to gravity vary with latitudinal position on earth.
The value of will be
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4
Problem on gravitational field due to different arrangements of shells and spheres.
Gravitational potential energy developed in the system of stationary bodies, when they are moved in space. Here energy is conserved because there are no external forces applied to the system. Students should keep this concept of energy conservation while solving the problem.
Two hypothetical planets of masses and are at rest when they are infinite distance apart. Because of the gravitational force they move towards each other along the line joining their centres. What is their speed when their separation is ?
(Speed of is and that of is )
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5
State and use Kepler's third law of planetary motion.
This is a tricky question, in this type of question we firstly predict the trajectory of the motion. Then calculate the time period based on the Kepler's Law.
India's Mangalyan was sent to the Mars by launching it into a transfer orbit EOM around the sun. It leaves the earth at E and meets Mars at M. If the semi-major axis of Earth's orbit is , that of Mars's orbit taken Kepler's laws give the estimate of time of Mangalyan to reach Mars from Earth to be close to :
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6
Binding Energy And Satellites
In this type of problem, relations between the two artificial bodies rotating around a heavenly body are given. We have to calculate the unknown value based on the binding energy concept.
The speed of a satellite that revolves around earth at a height from earth's surface is
m/s at the surface of earth, radius of earth km)
A
km s
B
km s
C
km s
D
km s