Question

A particle moves in x-y plane according to rule
x = a sinwt and y = a coswt. The particle follows
[AIPMT (Mains)-2010]
(1) An elliptical path
(2) A circular path
(3) A parabolic path
(4) A straight line path inclined equally to x and y-axes​

Answer 1

Answer:

option (4) is correct

Explanation:

since it is given that

A particle moves in x-y plane according to rule

x = a sinwt................(1) and y = a coswt.....................(2)

we know that resulatant vector is given as

$r=\sqrt{x^2+y^2+2xycos\alpha }$

where α is the angle between x and y axes which is 90°

so,

$r=\sqrt{x^2+y^2}$...............................(3)

put x and y from (1) and (2) in (3)

we get,

$r=\sqrt{a^2}$

as   $cos^2\beta +sin^2\beta =1$

so r=a........which is a straight line path inclined equally to x and y-axes.