Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : The kinetic energy needed to project a body of mass m from earth surface to infinity is 1/2 mgR, where R is the radius of earth.
Reason R : The maximum potential energy of a body is zero when it is projected to infinity from earth surface.
In the light of the above statements, choose the correct answer from the options given below

Solution

Physics sir · 4 steps

Work out the escape kinetic energy from energy conservation and you get mgR, not half of it.

1. Energy at the surface. On the surface the potential energy is U = -GMm/R. To just reach infinity, the body must arrive there with zero kinetic energy, where the potential energy is also zero.

   K - GMm/R = 0 ⇒ K = GMm/R = mgR

2. Check Assertion A. Using GM = gR², the kinetic energy needed is mgR. The value 1/2mgR is too small by a factor of 2, so A is false.
3. Check Reason R. Gravitational potential energy -GMm/r is negative at every finite r and rises towards zero as r → ∞. So its maximum value, reached at infinity, is zero, and R is true.
4. So. A is false and R is true, which is option (a).

The idea to keep. Escape kinetic energy equals the magnitude of the surface potential energy: GMm/R = mgR. Gravitational PE is always negative and climbs to its maximum, zero, at infinity.

Answer from the NTA final answer key. Solution by PrepWiser.