GravitationHard
Question
A solid sphere of uniform density and radius 4 units is located with its centre at the origin O of coordinates. Two spheres of equal radii 1 unit, with their centres at A ( - 2, 0, 0) and B (2, 0, 0) respectively, are taken out of the solid leaving behind spherical cavities as shown in figure.
Options
A.the gravitiational field at the point B (2, 0, 0) is zero
B.the gravitational field due to this object at the origin is zero
C.the gravitational potential is the same at all points of circle y2 + z2 = 36
D.the gravitiational potential is the same at all point s on the circle y2 + z2 = 4
Solution
(a) The gravitational field is zero at the centre of a solid sphere. The samll spheres can be considered as negative mass m located at A and B. The gravitational field due to these masses at O is equal and opposite. Hence, the resultant field at O is zero.
(c and d) → are correct because plane of these circles is y-z, i.e., perpendicular to x-axis i.e., potential at any point on these two circles will be equal to the positive mass M and negative masses - m and - m.
(c and d) → are correct because plane of these circles is y-z, i.e., perpendicular to x-axis i.e., potential at any point on these two circles will be equal to the positive mass M and negative masses - m and - m.
Create a free account to view solution
View Solution FreeMore Gravitation Questions
Gravitational potential at the centre of curvature of a hemispherical bowl of radius R and mass M is V : -...Calculate the mass of the sun if the mean radius of the earth′s orbit is 1.5 × 108 km and G = 6.67 × 10-...A small ball of mass ′m′ is released at a height ′R′ above the Earth surface, as shown in the fi...A man can jump to a height of 1.5 m on a planet A. What is the height he may be able to jump on another planet whose den...Weight of a body of mass m decreases by 1% when it is raised to height h above the Earth′s surface. If the body is...