The velocity of escape on a planet whose radius is 1.7 × 106 m and accelaration due to gravity is 1.7 m s-2 is

Question

The velocity of escape on a planet whose radius is 1.7 × 106 m and accelaration due to gravity is 1.7 m s-2 is (A)  1.7 Km s-1  (B)  2.89 Km s-1  (C)  1.7 √2 km s-1  (D)  3.4 Km s-1

Tardigrade Admin · Accepted Answer

Acceleration due to gravity on a planet, g' =1.7 m s-2 Radius of planet, r=1.7 × 106 m Escape velocity, vesc=√2g'r =√2×1.7×1.7×106 =1.7×103 √2 m s-1 =1.7√2 km s-1

Q. The velocity of escape on a planet whose radius is $1.7 \times 1 0^{6} m$ and accelaration due to gravity is $1.7 m s^{- 2}$ is

$1.7 K m s^{- 1}$

$2.89 K m s^{- 1}$

$1.7 2 km s^{- 1}$

$3.4 K m s^{- 1}$

Acceleration due to gravity on a planet,
$g^{'} = 1.7 m s^{- 2}$
Radius of planet, $r = 1.7 \times 1 0^{6} m$
Escape velocity, $v_{esc} = 2 g^{'} r$
$= 2 \times 1.7 \times 1.7 \times 1 0^{6}$
$= 1.7 \times 1 0^{3} 2 m s^{- 1}$
$= 1.7 2 km s^{- 1}$

Q. The velocity of escape on a planet whose radius is 1.7×106m and accelaration due to gravity is 1.7ms−2 is

1.7Kms−1

2.89Kms−1

1.72​kms−1

3.4Kms−1