If the radius of a planet is $$R$$ and its density is $$\rho$$, the escape velocity from its surface will be:
1. $$v_e\propto \rho R$$
2. $$v_e\propto \sqrt{\rho} R$$
3. $$v_e\propto \frac{\sqrt{\rho}}{R}$$
4. $$v_e\propto \frac{1}{\sqrt{\rho} R}$$

Subtopic:  Escape velocity |
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For a planet having mass equal to the mass of the earth but radius equal to one-fourth of the radius of the earth, its escape velocity will be:
 1 $$11.2$$ km/s 2 $$22.4$$ km/s 3 $$5.6$$ km/s 4 $$44.8$$ km/s
Subtopic:  Escape velocity |
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AIPMT - 2000
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A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would Earth (mass$$=5.98\times 10^{24}~\text{kg})$$ have to be compressed to be a black hole?
1. $$10^{-9}~\text{m}$$
2. $$10^{-6}~\text{m}$$
3. $$10^{-2}~\text{m}$$
4. $$100​~\text{m}$$

Subtopic:  Escape velocity |
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AIPMT - 2014
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A projectile is fired upwards from the surface of the earth with a velocity $$kv_e$$ where $$v_e$$ is the escape velocity and $$k<1$$. If $$r$$ is the maximum distance from the center of the earth to which it rises and $$R$$ is the radius of the earth, then $$r$$ equals:
1. $$\frac{R}{k^2}$$
2. $$\frac{R}{1-k^2}$$
3. $$\frac{2R}{1-k^2}$$
4. $$\frac{2R}{1+k^2}$$

Subtopic:  Escape velocity |
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A body is projected vertically upwards from the surface of a planet of radius $$R$$ with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is:
1. $$\frac{R}{3}$$
2. $$\frac{R}{2}$$
3. $$\frac{R}{4}$$
4. $$\frac{R}{5}$$

Subtopic:  Escape velocity |
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A particle is located midway between two point masses each of mass $$M$$ kept at a separation $$2d.$$ The escape speed of the particle is: (neglect the effect of any other gravitational effect)
1. $$\sqrt{\frac{2 GM}{d}}$$
2. $$2 \sqrt{\frac{GM}{d}}$$
3. $$\sqrt{\frac{3 GM}{d}}$$
4. $$\sqrt{\frac{GM}{2 d}}$$

Subtopic:  Escape velocity |
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