Question

Reason
Escape velocity from the surface of earth is $$\sqrt {2gR}$$ where R is radius of earth.
Assertion
Escape velocity is independent of the angle of projection.
Escape velocity is independent of the angle of projection.

Answer 1

Correct option is A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

The gravitational field is conservative field.

So the energy required (kinetic) to get an object from earth surface to infinity is path independent.

This makes escape velocity independent of angle of projection.

As per the conservation of energy

Change in kinetic energy = change in gravitational potential energy

$$\Rightarrow$$ $$\dfrac{1}{2} mV^2 = \dfrac{GMm}{R}$$

$$\Rightarrow$$ $$v_{escape} = \sqrt{\dfrac{2GM}{R}}$$

$$\Rightarrow$$ $$v_{escape} = \sqrt{2gR}$$ [Where $$\dfrac{2GM}{R}$$ = $$g$$]