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Q.

An orbiting satellite will escape if
a) its speed increases by 41.4%
b) its speed in the orbit is made $\sqrt{1.414}$ times that of its initial value
c) its kinetic energy increases by 100%
d) its kinetic energy is made √2 times that of its initial value

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a

only a & b are correct

b

only a & c are correct

c

only b & c are correct

d

only c is correct

answer is B.

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Detailed Solution

For circular orbit , orbital soeed of the satellite $V_{0} = \sqrt{\frac{G M}{r}}$ .

Again escape velocity at any point on the circular orbit $V_{e} = \sqrt{\frac{2 G M}{r}}$

$\frac{V_{e} - V}{V} \times 100$ =41.4%.: Increase in Speed

Increase in K.E

$\frac{\frac{1}{2} m v_{e}^{2} - \frac{1}{2} m v^{2}}{\frac{1}{2} m v^{2}} \times 100$

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