How many kilometers make one light year?
`a) 9.4607 × 10^12 km`
`b) 9.4607 × 10^9 km`
`c) 9.4607 × 10^11 km`
`d) 9.4607 × 10^10 km`

Answer

A, B, C, D

Explanation

R=radius of the bridge
L=total lengthof the over bridge ltbr.a At the highest point
`mg=(mv^2)/r`
`rarr v^2=Rg`
`rarr v=sqrt(Rg)`

b. Given `v=(1/sqrt2)sqrt(Rg)`
Suppose it loses contact at B.
`So at B, mg costheta= (mv^2)/R`
`rarr v^2=Rgcostheta`
`rarr sqrt((Rg)/2)^2)=Rgcostheta`
`rarr (Rg)/2=Rg.costheta`
`-. costheta=1/2`
`rarr theta=60^0=pi/3`
`theta=1/R`
`rarr Rtheta=(pir)/3`
so it will lose contact at a distance `(pir)/3` from highest point.
c. Let the uniform speed on the bridge by v. The changes of losing contact is maximum at the end of the bridge for which,
`alpha=L/(2R)`
`So, (mv^2)/R=mgcosalpha`
`rarr v=sqrt(gRcos(L/(2R))`