NEETPhysicsGravitation
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): If a body is projected from the earth's surface at an angle of 45^ to the vertical, its escape velocity remains the same as when projected vertically upwards. Reason (R): Escape velocity depends only on the mass and radius of the planet and is independent of the mass of the body and the angle of pr
Options
- ABoth Assertion (A) and Reason (R) are correct but Reason (R) is not the correct explanation of Assertion (A).
- BAssertion (A) is correct but Reason (R) is incorrect.
- CBoth Assertion (A) and Reason (R) are correct and Reason (R) is the correct explanation of Assertion (A).
- DAssertion (A) is incorrect but Reason (R) is correct.
Correct answer
C. Both Assertion (A) and Reason (R) are correct and Reason (R) is the correct explanation of Assertion (A).
Step-by-step solution
The escape velocity of a body from the surface of a planet is given by v_e = 2GM R , where M is the mass of the planet and R is its radius. This expression is derived using the principle of conservation of mechanical energy. Since kinetic and potential energies are scalar quantities, the escape velocity is independent of the angle of projection and the direction in which the body is thrown. The formula also shows that v_e is independent of the mass of the projected body. Thus, both the Assertion and the Reason are