Question

The momentum needed to project a body of mass 5 kg from the surface of the Moon to infinity is ___________ kg m/s. (Take, the mass of the Moon = 7.3 × 10²² kg) (radius of the Moon = 1.74 × 10⁶ m)

• A. $14.45\times {10}^8\sqrt{G}$
• B. $14.45\times {10}^6\sqrt{G}$
• C. $14.45\times {10}^3\sqrt{G}$
• D. $14.45\times {10}^{-6}\sqrt{G}$

Answer 1

The correct option is A

$14.45\times {10}^8\sqrt{G}$

Step 1, Given data

Mass of the body = 5 kg

Mass of the moon = 7.3 × 10²² kg

Radius of the moon = 1.74 × 10⁶ m

Step 2, Finding the momentum

We know,

Momentum is given as $P=mv$

Body must be thrown with the escape velocity

So, $P=m{v}_e$

Or, $P=m\sqrt{\frac{2Gm}{R}}$

Putting all the values

$P=5\times \sqrt{\frac{2\times 7.3\times {10}^{22}G}{1.74\times {10}^{16}}}=5\times \sqrt{\frac{1.46\times {10}^{6}G}{1.74}}=5\times {10}^8\times \sqrt{8.39G}=5\times {10}^8\times 2.89\sqrt{G}=14.45\times {10}^8\sqrt{G}$

Therefore the momentum is $14.45\times {10}^8\sqrt{G}$

Hence the correct option is (A).