Advertisements
Advertisements
Question
A thin spherical shell having uniform density is cut in two parts by a plane and kept separated as shown in the following figure. The point A is the centre of the plane section of the first part and B is the centre of the plane section of the second part. Show that the gravitational field at A due to the first part is equal in magnitude to the gravitational field at B due to the second part.
Solution
We know that in a thin spherical shell of uniform density, the gravitational field at its internal point is zero. So, at points A and B, the gravitational fields are equal and opposite and, thus, cancel each other. So the net field is zero.
Hence, EA = EB
APPEARS IN
RELATED QUESTIONS
How does the force of gravitation between two objects change when the distance between them is reduced to half?
State Kepler’s law which is represented by the relation r3 ∝ T2.
State the universal law of gravitation. Name the scientist who gave this law.
Universal law of gravitation states that every object exerts a gravitational force of attraction on every other object. If this is true, why don’t we notice such forces ? Why don’t the two objects in a room move towards each other due to this force ?
Write the three laws given by Kepler. How did they help Newton to arrive at the inverse square law of gravity?
Three equal masses m are placed at the three corners of an equilateral triangle of side a. Find the force exerted by this system on another particle of mass m placed at (a) the mid-point of a side, (b) at the centre of the triangle.
Two small bodies of masses 10 kg and 20 kg are kept a distance 1.0 m apart and released. Assuming that only mutual gravitational forces are acting, find the speeds of the particles when the separation decreases to 0.5 m.
Derive an expression for the gravitational field due to a uniform rod of length L and mass M at a point on its perpendicular bisector at a distance d from the centre.
The mass of moon is about 0.012 times that of earth and its diameter is about 0.25 times that of earth. The value of G on the moon will be:
Explain the following:
People often shake the branches of a tree for getting down its fruits.
A ball is thrown vertically upwards. It goes to a height 20 m and then returns to the ground. Taking acceleration due to gravity g to be 10 ms-2 , find :
the total time of journey of the ball .
How will the force of gravitation between two objects change if the distance between them is:
Made four times
How will the force of gravitation between two objects change if the distance between them is:
Infinite
Does the force of the earth's gravitation affect the motion of the moon? Explain your answer with reasons.
State Newton's law of gravitation. What is the difference between:
g and G?
Mahendra and Virat are sitting at a distance of 1 m from each other.Their masses are 75 kg and 80 kg respectively. What is the gravitational force between them? (G = 6.67 × 10-11 Nm2/kg2)
For the weight of body of mass 5 kg to be zero on equator of the earth, angular velocity of the earth must be (The radius of earth = 6400 km, acceleration due to gravity = 10 m/s2).
Three uniform spheres, each having mass m and radius r, are kept in such a way that each touches the other two. The magnitude of the gravitational force on any sphere due to the other two is
If the law of gravitation, instead of being inverse-square law, becomes an inverse-cube law- ______.
- planets will not have elliptic orbits.
- circular orbits of planets is not possible.
- projectile motion of a stone thrown by hand on the surface of the earth will be approximately parabolic.
- there will be no gravitational force inside a spherical shell of uniform density.
