Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation

A tunnel is excavated along a diameter of the Earth. Determine the force acting on a particle of mass m positioned in the tunnel at a distance x from the centre.

Options

  1. AG M_e m x^2
  2. BG M_e m x^2 R^4
  3. CG M_e m R^3 x
  4. DG M_e m R^2 x

Correct answer

C. G M_e m R^3 x

Step-by-step solution

The mass of the Earth enclosed within a sphere of radius x is given by M' = M_e 4 3 R^3 ( 4 3 x^3 ) = M_e x^3 R^3 . The gravitational force acting on a particle of mass m at a distance x from the centre is due only to the mass enclosed within the sphere of radius x . Using Newton's law of gravitation, the force is F = G M' m x^2 . Substituting the value of M' , we get F = G ( M_e x^3 R^3 ) m x^2 = G M_e m R^3 x .

Practice Gravitation on Quantrex Academy →

More from Gravitation

A particle of mass m , and angular momentum is moving in a circular orbit of radius r₀ under the influence of an attractive force F (r) = - k r^2 r . Keeping its angular momentum u 2026A body of mass m is taken from the surface of earth to a height equal to twice the radius of earth ( R_e ). The increase in potential energy will be _______. ( g is acceleration du 2026When one moves from a point 16 km below the earth's surface to a point 16 km above the earth's surface. The change in g is approximately %. The value of is _____. (Take radius of t 2026The height in terms of radius of the earth (R) , at which the acceleration due to gravity becomes g 9 , where g is acceleration due to gravity on earth's surface, is ______. 2026If a body of mass 1 kg falls on the earth from infinity, it attains velocity (v) and kinetic energy (k) on reaching the surface of earth. The values of v and k respectively are ___ 2026A planet (P₁) is moving around the star of mass 2M in the orbit of radius R . Another planet (P₂) is moving around another star of mass 4M in a orbit of radius 2R . Ratio of time p 2026Three masses 200 ~kg , 300 ~kg and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m. They are rearranged on the vertices of a bigger triangle of side 25 2026Given below are two statements: Statement I : A satellite is moving around earth in the orbit very close to the earth surface. The time period of revolution of satellite depends up 2026 Full Gravitation list All Concepts Of Physics MCQ Edition [Volume 1] PYQs