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Statement 1: The value of escape velocit...

Statement 1: The value of escape velocity from the surface of earth at `30^@` and `60^@` is `v_(1)=2v_(e), v_(2)=2//3v_(e)`.
Statement II: The value of escape velocity is independent of angle of projection.

A

Statement I is True, Statement II is True: Statement II is a correct explanation for Statement I.

B

Statement I is True, Statement II is True: Statement II is Not a correct explanation for Statement I.

C

Statement I is True, Statement II is False.

D

Statement I is False, Statement II is True.

Text Solution

Verified by Experts

The correct Answer is:
D
The value of escape velocity is derived from the method of conservation of total mechanical energy and energy is independnet of direction.
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Statement I: If a particle projected horizontally just above, the surface of the earth with a speed greater than escape speed, then it will escape from gravitational influence of the earth. Assume that particle has a clear path. Statement II: Escape velocity is independent of its direction.

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Knowledge Check

  • The escape velocity from the surface of the earth is (where R_(E) is the radius of the earth )

    A
    `sqrt(2gR_(E))`
    B
    `sqrt(gR_(E))`
    C
    `2sqrt(gR_(E))`
    D
    `sqrt(3gR_(E))`

  • The escape velocity from earth is 11.2 km per sec. If a body is to be projected in a direction making an angle 45^(@) to the vertical, then the escape velocity is

    A
    `11.2 xx 2` km/sec
    B
    `11.2` km/sec
    C
    `11.2 xx (1)/(sqrt(2))` km/sec
    D
    `11.2 xx sqrt(2)` km/sec

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