What is a vector quantity?
a) A quantity with only magnitude
b) A quantity with only direction
c) A quantity with both magnitude and direction
d) A quantity without direction

Answer

B, C, D

Explanation

a. When the particle is released from rest ure the centrifugal force is zero.
N force =`mgcostheta=mgcos30^0`
`=sqrt3/2`mg
b. When the particle leaves contact with the surface ure `N=theta`

`So, (mv^2)/R=mgcostheta`
`rarr v^2=Rcostheta` ........i
`Again
(1/2)mv^2=mgR(cos30^0-costheta)`
`rarr v^2=2rg(sqrt3/2-costheta)`........ii
`from equation i and equation ii
`Rgcostheta=2Rg[sqrt3/2-costheta]`
`rarr 3costheta=sqrt(3)`
`rarr costheta=1/sqrt3`
`or theta=cos^-1 1/sqrt3`
so, the distance travelld by the particle before leaving contact
`L=R(theta-pi/6)`
[because `30^0=(pi/6)`]
`putting the value of theta we get`
`L=0.43R`