Question

A particle balls towards earth from infinity. Its velocity on reaching the earth will be (R is redius of earth)

Answer 1

Heya user☺☺

We can see this from the expression for the potential energy at a distance rr:

V=−GMmr


For the Sun M=1.9891×1030M=1.9891×1030 kilograms and rr (the orbital radius of the Earth) ≈1.5×1011≈1.5×1011 so V≈8.85×108mV≈8.85×108m J.

For the Earth M=5.97219×1024M=5.97219×1024 kilograms and rr (the radius of the Earth) ≈6.4×106≈6.4×106 so V≈6.15×107mV≈6.15×107m J.

So the effect of the Sun's gravity is about 14 times greater. The velocity of the comet will be given by:

12mv2=(8.85×108+6.15×107)m12mv2=(8.85×108+6.15×107)m

which gives:

v≈43.5km/sec


Hope this will help☺☺