Question

A particle moves so that its position vector is given
by r = cos ot x + sinot y, where o is a constant.
Which of the following is true? [NEET-2016]
(1) Velocity is perpendicular to r and acceleration
is directed away from the origin
(2) Velocity and acceleration both are
perpendicular to r
(3) Velocity and acceleration both are parallel to r
(4) Velocity is perpendicular tor and acceleration
is directed towards the origin​

Answer 1

Hey Dear,

◆ Answer -

(4) Velocity is perpendicular tor and acceleration is directed towards the origin

● Explaination -

Given that r = cos(ot.x) + sin(ot.y)

Now, velocity is calculated as -

v = dr/dt

v = d/dt [cos(ot.x) + sin(ot.y)]

v = -o.sin(ot.x) - o.cos(ot.y)

Acceleration is calculated as -

a = dv/dt

a = d/dt [-o.sin(ot.x) - o.cos(ot.y)]

a = -o².cos(ot.x) - o².sin(ot.x)

a = -o² [cos(ot.x) + sin(ot.y)]

a = -o².r

As position vector is directed away from the origin, acceleration will be directed towards the origin. Only option with thiz possibility is option (4).

* You can verify that velocity is perpendicular to radius by taking dot product r.v = 0.

Thanks dear...

Answer 2

Answer:

Here is the answer :

Explanation: