Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT2020PhysicsGravitationActual

The escape velocity from a planet is v_ e . A tunnel is dug along a diameter of the planet and a small body is dropped into it at the surface. When the body reaches the centre of the planet, its speed will be

Options

  1. AV _ e
  2. Bv _ e / 2
  3. Cv _ e / 2
  4. Dzero

Correct answer

B. v _ e / 2

Step-by-step solution

1 2 mv _ e ²= GMm R ; v _ e = GMm R = 2 gR In tunnel body will perform SHM at centre V _ max = A (see chapter on SHM) = R 2 2 R / g = gR = v _ e 2

Practice Gravitation on Quantrex Academy →

More from Gravitation

A body which is initially at rest at a height R above the surface of the Earth of radius R, falls freely towards the Earth, then its velocity on reaching the surface of the Earth i 2024The distance between Sun and Earth is R . The duration of year if the distance between Sun and Earth becomes 3 R will be: 2024For a particle inside a uniform spherical shell, the gravitational force on the particle is 2024The kinetic energy of a satellite in its orbit around the earth is E . What should be the kinetic energy of the satellite so as to enable it to escape from the gravitational pull o 2024Two identical particles each of mass ' m ' go round a circle of radius a under the action of their mutual gravitational attraction. The angular speed of each particle will be: 2023If V is the gravitational potential due to sphere of uniform density on it's surface, then it's value at the center of sphere will be: 2023Two planets A and B of radii R and 1.5 R have densities and / 2 respectively. The ratio of acceleration due to gravity at the surface of B to A is : 2023Suppose the law of gravitational attraction suddenly changes and becomes an inverse cube law i.e. F 1 r³ , but still remaining a central force. Then 2021 Full Gravitation list All BITSAT PYQs