If a body of mass 1 kg falls on the earth from infinity, it attains velocity and kinetic energy on reaching the surface of earth

Question

If a body of mass 1 kg falls on the earth from infinity, it attains velocity $(v)$ and kinetic energy $(k)$ on reaching the surface of earth. The values of $(v)$ and $(k)$ respectively are _________. [2026]

(Take radius of earth to be 6400 km and $g = 9.8 m / s^{2}$ )

Smart Achievers · Accepted Answer

(1)

$Conserving mechanical energy,$

$(k)$

$g = 9.8 m / s^{2}$

$v = \sqrt{\frac{2 G M}{R_{e}}} = \sqrt{2 g R_{e}}$

$= \sqrt{2 \times 9.8 \times 6.4 \times 10^{6}}$

$= \sqrt{1.2544 \times 10^{8}} = 11200 m / s$

$Kinetic energy \frac{1}{2} m v^{2} = 6.27 \times 10^{7} J$

Solution

Q.
If a body of mass 1 kg falls on the earth from infinity, it attains velocity $(v)$ and kinetic energy $(k)$ on reaching the surface of earth. The values of $(v)$ and $(k)$ respectively are _________. [2026]

(Take radius of earth to be 6400 km and $g = 9.8 m / s^{2}$ )

1 $11.2 km / s; 6.27 \times 10^{7} J$

2 $11.2 km / s; 12.54 \times 10^{7} J$

3 $8.8 km / s; 6.27 \times 10^{7} J$

4 $8.8 km / s; 12.54 \times 10^{7} J$

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Solution

Q. If a body of mass 1 kg falls on the earth from infinity, it attains velocity (v) and kinetic energy (k) on reaching the surface of earth. The values of (v) and (k) respectively are _________. [2026] (Take radius of earth to be 6400 km and g=9.8 m/s2)

1 11.2 km/s; 6.27×107 J

2 11.2 km/s; 12.54×107 J

3 8.8 km/s; 6.27×107 J

4 8.8 km/s; 12.54×107 J