Consider the motion of a particle described by ` x = a cos t , y= a sin t and z=t ` . The trajectory traced by the particle as a function of time is

Options

A. helix
B. circular
C. elliptical
D. straight line

Answer

A

Explanation

Given ,
` x= " acost "`
` y= " asint"`
and z=t
path is circular in xy - plane ,
`(x^2 )/( a^2 ) +(y^2)/( a^2)= cos ^2 theta + sin ^2 theta `
` ( x^2 )/(a^2) +(y ^2)/(b^2)=1`
in one revoluation the particle move a distance of 1 unit along z - axis
`( dz )/( dt) =1 `
hence , path is helix .