Q.1. Calculate the change in the value of g at altitude 45°. Take radius of earth = 6.37 × 10^{3} km
Sol.
= g 0.0168 m/s^{2}
Dg = gg' = 0.0168 m/s^{2 }
Q.2. Determine the speed with which the earth would have to rotate on its axis, so that a person on the equator would weigh 3/5th as much as at present. Take R = 6400 km
Sol.
Q.3. At what height from the surface of earth will the value of g be reduced by 36% from the value at the surface? R = 6400 km
Sol.
Q.4. The distance between two bodies A and B is r. Taking the gravitational force according to the law of inverse square of r, the acceleration of the body A is a. If the gravitational force follows an inverse fourth power law, then what will be the acceleration of body A?
Sol.
Q.5. Find the force of attraction on a particle of mass m placed at the centre of a semicircular wire of length L and mass M.
Sol.
Q.1. A particle of mass m is placed at the centre of a uniform spherical shell of same mass and radius R. Find the gravitational potential at a distance R/2 from the centre.
Sol.
V = V_{e }+ V_{s} =
Q.2. A particle of mass 20 g experiences a gravitational force of 4.0 N along positive xdirection. Find the gravitational field at that point.
Sol.
200 N/kg i
Q.3. The gravitational potential due to a mass distribution is V = 3x^{2}y + y^{3}z. Find the gravitational field.
Sol.
Q.4. Gravitational potential at x = 2 m is decreasing at a rate of 10 J/kgm along the positive xdirection. It implies that the magnitude of gravitational field at x = 2 m is also 10 N/kg. Is this statement true or false?
Sol. Only the variation is given along xaxis, nothing is about y and z axis, so, the statement is false.
Q.5. The gravitational potential in a region is given by, V = 20(x+ y) J/kg. Find the magnitude of the gravitational force on a particle of mass 0.5 kg placed at the origin.
Sol.
Q.6. The gravitational field in a region is given by
Find the work done by the gravitational field when a particle of mass 1 kg is moved on the line 3y + 2x = 5 from (1 m, 1 m) to (2 m, 3 m).
Sol.
102 videos411 docs121 tests

1. What is the formula for gravitational force? 
2. How does the distance between two objects affect the gravitational force between them? 
3. What is the significance of the gravitational constant in the formula for gravitational force? 
4. What is the difference between mass and weight in the context of gravity? 
5. How does the gravitational force affect the motion of celestial bodies in the universe? 

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