# If escape velocity from the earth’s surface is 11.2 km/sec. then escape velocity from a planet of mass same as that of earth but radius one fourth as that of earth is Option 1) 11.2 km/sec Option 2) 22.4 km/sec Option 3) 5.65 km/sec Option 4) 44.8 km/sec

As we learnt in

Escape velocity ( in terms of radius of planet) -

$V_{c}=\sqrt{\frac{2GM}{R}}$

$V_{c}=\sqrt{2gR}$

$V_{c}\rightarrow$ Escape velocity

$R\rightarrow$Radius of earth

- wherein

• depends on the reference body
• greater the value of $\frac{M}{R}$ or $\left ( gR \right )$ greater will be the escape velocity $V_{e}=11.2Km/s$  For earth

Escape velocity$=\sqrt{\frac{2GM}{R}}$

$\frac{V_{p}}{V_{e}}=\sqrt{\frac{R_{e}}{R_{p}}}=2$

$\therefore V_{p}= 22.4 km/sec$

Option 1)

11.2 km/sec

This is incorrect option

Option 2)

22.4 km/sec

This is correct option

Option 3)

5.65 km/sec

This is incorrect option

Option 4)

44.8 km/sec

This is incorrect option

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