The radius in kilometer to which the present radius of earth ( R =6400 km ) to be compressed so that the escape velocity is increased 10 time is .

Question

The radius in kilometer to which the present radius of earth ( R =6400 km ) to be compressed so that the escape velocity is increased 10 time is . (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

V e =√(2 Gm / R ) ldots (1) 10 V e =√(2 Gm / R prime) ldots (2) ∴ 10=√( R / R prime) ⇒ R prime=( R /100)=(6400/100)=64 km

Q. The radius in kilometer to which the present radius of earth $(R = 6400 km)$ to be compressed so that the escape velocity is increased $10$ time is ________.

$V_{e} = \frac{2 G m}{R} \dots$ (1)
$10 V_{e} = \frac{2 G m}{R ^{'}} \dots$ (2)
$∴ 10 = \frac{R}{R ^{'}}$
$\Rightarrow R^{'} = \frac{R}{100} = \frac{6400}{100} = 64 km$

Q. The radius in kilometer to which the present radius of earth (R=6400km) to be compressed so that the escape velocity is increased 10 time is ________.

Ve​=R2Gm​​… (1) 10Ve​=R′2Gm​​… (2) ∴10=R′R​​ ⇒R′=100R​=1006400​=64km

Q. The radius in kilometer to which the present radius of earth $(R = 6400 km)$ to be compressed so that the escape velocity is increased $10$ time is ________.

$V_{e} = \frac{2 G m}{R} \dots$ (1)
$10 V_{e} = \frac{2 G m}{R ^{'}} \dots$ (2)
$∴ 10 = \frac{R}{R ^{'}}$
$\Rightarrow R^{'} = \frac{R}{100} = \frac{6400}{100} = 64 km$