Question

A coordinate of a particle moving in a plane are given by x=4cos10t and y=3sin10t​

Answer 1

Answer:

Solution

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Correct option is

D

Distance travelled by the particle in time interval between t=0 and t=

2P

π

is a

x=acos(pt),y=bsin(pt)

∴

a

2

x

2

+

b

2

y

2

=1, i.e., equation of ellipse

Now, r=x

i

^

+y

j

^

=acos(pt)

i

^

+bsin(pt)

j

^

v=

dt

dr

=−pasin(pt)

i

^

+pbcos(pt)

j

^

a=

dt

dv

=−p

2

acos(pt)

i

^

=p

2

bsin(pt)

j

^

at t=

2p

π

v=−pa

i

^

and a=−p

2

b

j

^

v perpendicular to a

Also, a=−p

2

r, i.e., directed towards a fixed point.