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$\frac{1}{2}mgR$, 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 option given below

Related Formula

Escape kinetic energy requirement formulation:

Gravitational potential energy field definition:

At r → ∞$r \to \infty$, Umax = 0$U_{\text{max}} = 0$.

Core Logic

• Assertion Check: The minimum work required to project an object from Earth's surface (r = R$r = R$) to infinity (r → ∞$r \to \infty$) equals the change in gravitational potential energy:

Therefore, the required kinetic energy is mgR$mgR$. The statement asserts it is (1)/(2)mgR$\frac{1}{2}mgR$ (which corresponds to orbital kinetic energy near Earth's surface). Hence, Assertion A is false.

• Reason Check: Since the gravitational force is attractive, potential energy is negative everywhere in the field and reaches its maximum value asymptotically at infinity (Umax = 0$U_{\text{max}} = 0$). Hence, Reason R is true.

Pattern Recognition

Escape energy from the surface is mgR$mgR$, while circular orbital kinetic energy near the surface is (1)/(2)mgR$\frac{1}{2}mgR$. Because gravitational potential energy is defined with zero at infinity, every bound state has U < 0$U < 0$, making zero the absolute maximum potential energy.

Evaluation Rubric / Model Answer

Option A: A is false but R is true

Chapter Mix

Class 11 Physics: Gravitation