A prtile is fired vertically upwrd with a speed of `15 kms^-1`. With what speed will it move it intarsteller space. Assume only earth's gravitational field.

Answer

A

Explanation

Initial velocity of the particle `=15 km/s`
let its speed be V at intesteller space
`=:.(1/2)m[15xx10^3-V^2]=int_R^oo (GMm)/x^2dx`
rarr (1/2)m[(15xx10^3)^2-V^2]=GMm[(-1)/x]`
`rarr (1/2)m[(225xx10^5)-v^2]=(GMm)/R`
`rarr 225xx10^5-v^2=(2xx6.67xx6xx10^24)/(6400xx10^3)`
`rarr v^2=225xx10^6-40.02/32xx10^8`
`=2.25xx10^8-1.2xx10^8`
`=10^98(1.05)`
`or v=1.01xx10^4m/s`
`=10 km/s`