UPSEE 2019 Solved Paper

Here, linear momentum of a particle
p=A(

^

i

‌cos‌bt−

^

j

‌sinbt) .......(i)
where, A and B are constants.
As we know that,
F=

dp

dt

From Eq. (i), we get
⇒F=

d

dt

(A

^

i

‌cos‌b‌t−A

^

j

‌sin‌b‌t)
⇒F=−A

^

i

b‌sin‌b‌t−A

^

j

b‌cos‌b‌t
Now, dot product =F.p
=(−A

^

i

b‌sin‌b‌t−A

^

j

b‌cos‌b‌t). (A

^

i

‌cos‌b‌t−A

^

j

‌sin‌b‌t)
=−Ab‌sin‌b‌t‌cos‌b‌t+Ab‌sin‌b‌t‌cos‌b‌t
=0
Since, F.p=Fp‌cos‌θ=0
⇒cos‌θ=0⇒θ=90°
Hence, the angle between momentum p and force F is 90°.