Assertion (A): Escape velocity of a satellite is greater than its orbital velocity.
Reason (R): Orbit of a satellite is within the gravitational field of planet whereas escaping is beyond the gravitational field of planet.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true: escape velocity \(V_e = \sqrt{2GM/r}\) is \(\sqrt{2}\) times orbital velocity \(V_o = \sqrt{GM/r}\) for a circular orbit.
Reason (R) is false because the gravitational field extends infinitely. Escaping means overcoming the gravitational potential, not leaving the field.
Assertion (A): Escape velocity from surface of a planet is \(V_e\). If a tunnel is made inside the surface, the escape velocity from a point inside the tunnel must be greater than \(V_e\).
Reason (R): Gravitational force is a conservative central force.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true; the gravitational potential energy is more negative (deeper well) inside a uniform planet, requiring greater escape velocity.
Reason (R) is true and foundational: gravity being a conservative central force allows the definition and calculation of potential energy and escape velocity.