An asteroid is moving directly towards the centre of the earth. When at a distance of 10R(R is the radius of the earth) from the earth’s centre, it has a speed of 12 km/s. Neglecting the effect of earth’s atmosphere, what will be the speed of the asteroid when it hits the surface of the earth (escape velocity from the earth is 11.2 km/s)? Give your answer to the nearest integer in kilometer/s-------

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

answer is 16.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

$\begin{array}{l} A p p l y i n g C o n s e r v a t i o n o f E n e r g y, \\ U_{i} + K_{i} = U_{f} + K_{f} \\ \Rightarrow - \frac{G M m}{10 R} + \frac{1}{2} m {(12 \times 10^{3})}^{2} = \frac{- G M m}{R} + \frac{1}{2} m {υ_{f}}^{2} \\ \Rightarrow \frac{1}{2} m {υ_{f}}^{2} = \frac{9 G M m}{10 R} + \frac{1}{2} m {(12 \times 10^{3})}^{2} \\ \Rightarrow {υ_{f}}^{2} = \frac{18 G M}{10 R} + {(12 \times 10^{3})}^{2} \\ \Rightarrow {υ_{f}}^{2} = \frac{9 \times 2 G M}{10 R} + {(12 \times 10^{3})}^{2} \\ \Rightarrow υ_{f} = \sqrt{\frac{9 {(V_{e})}^{2}}{10} + {(12 \times 10^{3})}^{2}} \\ \Rightarrow υ_{f} = \sqrt{\frac{9 {(11.2 \times 10^{3})}^{2}}{10} + {(12 \times 10^{3})}^{2}} [E s c a p e V e l o c i t y = V_{e} = \sqrt{\frac{2 G M}{R}} = 11.2 k m / s] \\ \Rightarrow υ_{f} = \sqrt{112 + 144} \times 10^{3} m / \sec \\ \Rightarrow υ_{f} = 16 k m / \sec \end{array}$

Watch 3-min video & get full concept clarity

tricks from toppers of Infinity Learn

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET