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Concepts Of Physics MCQ Edition [Volume 1]PhysicsGravitation

A mass of 6 10²⁴ kg (equivalent to the mass of the earth) is to be compressed into a sphere such that the escape velocity from its surface reaches 3 10^8 m/s . Determine the required radius of the sphere.

Options

  1. A18 mm
  2. B4.5 mm
  3. C9 mm
  4. D9 cm

Correct answer

C. 9 mm

Step-by-step solution

The escape velocity from the surface of a sphere of mass M and radius R is given by: v_e = 2GM R Rearranging the formula to solve for the radius R : R = 2GM v_e^2 Substituting the given values M = 6 10²⁴ kg , v_e = 3 10^8 m/s , and G = 6.67 10⁻¹¹ N m ^2 /kg ^2 : R = 2 6.67 10⁻¹¹ 6 10²⁴ (3 10^8)^2 R = 80.04 10¹³ 9 10¹⁶ R = 8.89 10⁻³ m R 9 mm

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