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Gravitation

Section: Physics

Question : 14 of 22

Marks: +1, -0

The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is 4 $\sqrt{ \frac{GM}{L} }$
The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is 2 $\sqrt{ \frac{GM}{L} }$
The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is $\sqrt{ \frac{2GM}{L} }$
The energy of the mass m remains constant

Solution:

\frac{1}{2} m v^2_{\text{min}} + m\left[ -\frac{\text{GM}}{L} \times 2 \right] = 0

energy conservation

\frac{v^2_{\text{min}}}{2} = \frac{2\text{GM}}{L}

v_{\text{min}} = 2 \sqrt{ \frac{\text{GM}}{L} }

as (B)

Total energy of mass does not remain constant as net force on it is non-zero

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